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#BSCTrendingCoins / Mathematics Textbook & Expert-Verified What are all values of k for which the graph y=x 3 −3x 2 +k will have three distinct x-intercepts? Asked by supergirl3210 • 05/07/2023 0:20 / 0:38 Community Answer This answer helped 7731810 people 7M 4.0 0 Values of k for which the **graph **y = x³ - 3x² + k will have three distinct x - intercepts are given by 0 < k < 4. Given the **function **of the **graph **is, y = x³ - 3x² + k, where k is constant. **Differentiating **the function with respect to 'x' we get, y' = 3x² - 6x y'' = 6x - 6 Now, y' = 0 gives 3x² - 6x = 0 x² - 2x = 0 x(x - 2) = 0 x = 0, 2 Now, for x = 0, y''(0) = -6 < 0, so at this point the function has maximum value. and for x = 2, y''(2) = 12 - 6 = 6 > 0, so at this point the function has minimum value. So, max y = y(0) = k > 0 min y = y(2) = 8 - 12 + k = k - 4 < 0 So, k < 4 Hence the values are, 0 < k < 4.
#BSCTrendingCoins
/
Mathematics
Textbook & Expert-Verified
What are all values of k for which the graph y=x
3
−3x
2
+k will have three distinct x-intercepts?

Asked by supergirl3210 • 05/07/2023
0:20
/
0:38
Community Answer
This answer helped 7731810 people

7M
4.0
0
Values of k for which the **graph **y = x³ - 3x² + k will have three distinct x - intercepts are given by 0 < k < 4.

Given the **function **of the **graph **is,

y = x³ - 3x² + k, where k is constant.

**Differentiating **the function with respect to 'x' we get,

y' = 3x² - 6x

y'' = 6x - 6

Now, y' = 0 gives

3x² - 6x = 0

x² - 2x = 0

x(x - 2) = 0

x = 0, 2

Now, for x = 0, y''(0) = -6 < 0, so at this point the function has maximum value.

and for x = 2, y''(2) = 12 - 6 = 6 > 0, so at this point the function has minimum value.

So, max y = y(0) = k > 0

min y = y(2) = 8 - 12 + k = k - 4 < 0

So, k < 4

Hence the values are, 0 < k < 4.
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ETF stands for Exchange-Traded Fund, which is a type of investment fund that trades on stock exchanges like a stock. ETFs can track various assets, including stocks, bonds, commodities, or cryptocurrencies. Are you asking about a specific ETF, such as a crypto ETF (like a Bitcoin or BNB ETF), or traditional stock market ETFs? Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain. Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges.
ETF stands for Exchange-Traded Fund, which is a type of investment fund that trades on stock exchanges like a stock. ETFs can track various assets, including stocks, bonds, commodities, or cryptocurrencies.

Are you asking about a specific ETF, such as a crypto ETF (like a Bitcoin or BNB ETF), or traditional stock market ETFs?

Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain.

Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges.
#SECCrypto2.0 Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain. Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges. Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain. Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges. Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain. Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges.
#SECCrypto2.0
Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain.

Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges.

Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain.

Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges.

Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain.

Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges.
$ETH ETF stands for Exchange-Traded Fund, which is a type of investment fund that trades on stock exchanges like a stock. ETFs can track various assets, including stocks, bonds, commodities, or cryptocurrencies. Are you asking about a specific ETF, such as a crypto ETF (like a Bitcoin or BNB ETF), or traditional stock market ?
$ETH
ETF stands for Exchange-Traded Fund, which is a type of investment fund that trades on stock exchanges like a stock. ETFs can track various assets, including stocks, bonds, commodities, or cryptocurrencies.

Are you asking about a specific ETF, such as a crypto ETF (like a Bitcoin or BNB ETF), or traditional stock market ?
#BinanceEarnYieldArena Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain. Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges. jj
#BinanceEarnYieldArena
Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain.

Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges.

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#SECCryptoRoundtable ETF stands for Exchange-Traded Fund, which is a type of investment fund that trades on stock exchanges like a stock. ETFs can track various assets, including stocks, bonds, commodities, or cryptocurrencies. Are you asking about a specific ETF, such as a crypto ETF (like a Bitcoin or BNB ETF), or traditional stock market ETFs? ETF stands for Exchange-Traded Fund, which is a type of investment fund that trades on stock exchanges like a stock. ETFs can track various assets, including stocks, bonds, commodities, or cryptocurrencies. Are you asking about a specific ETF, such as a crypto ETF (like a Bitcoin or BNB ETF), or traditional stock market ETFs? ETF stands for Exchange-Traded Fund, which is a type of investment fund that trades on stock exchanges like a stock. ETFs can track various assets, including stocks, bonds, commodities, or cryptocurrencies. Are you asking about a specific ETF, such as a crypto ETF (like a Bitcoin or BNB ETF), or traditional stock market ETFs?
#SECCryptoRoundtable
ETF stands for Exchange-Traded Fund, which is a type of investment fund that trades on stock exchanges like a stock. ETFs can track various assets, including stocks, bonds, commodities, or cryptocurrencies.

Are you asking about a specific ETF, such as a crypto ETF (like a Bitcoin or BNB ETF), or traditional stock market ETFs?

ETF stands for Exchange-Traded Fund, which is a type of investment fund that trades on stock exchanges like a stock. ETFs can track various assets, including stocks, bonds, commodities, or cryptocurrencies.

Are you asking about a specific ETF, such as a crypto ETF (like a Bitcoin or BNB ETF), or traditional stock market ETFs?

ETF stands for Exchange-Traded Fund, which is a type of investment fund that trades on stock exchanges like a stock. ETFs can track various assets, including stocks, bonds, commodities, or cryptocurrencies.

Are you asking about a specific ETF, such as a crypto ETF (like a Bitcoin or BNB ETF), or traditional stock market ETFs?
#ETFWatch ETF stands for Exchange-Traded Fund, which is a type of investment fund that trades on stock exchanges like a stock. ETFs can track various assets, including stocks, bonds, commodities, or cryptocurrencies. Are you asking about a specific ETF, such as a crypto ETF (like a Bitcoin or BNB ETF), or traditional stock market ETFs? Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain. Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges.
#ETFWatch ETF stands for Exchange-Traded Fund, which is a type of investment fund that trades on stock exchanges like a stock. ETFs can track various assets, including stocks, bonds, commodities, or cryptocurrencies.

Are you asking about a specific ETF, such as a crypto ETF (like a Bitcoin or BNB ETF), or traditional stock market ETFs?

Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain.

Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges.
$BNB Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain. Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges.
$BNB Binance Coin (BNB) is the native cryptocurrency of the Binance ecosystem, including the Binance Exchange and Binance Smart Chain (now BNB Chain). Initially launched on the Ethereum blockchain in 2017, BNB later migrated to Binance's own blockchain. It serves multiple purposes, such as paying for transaction fees on the Binance Exchange, participating in token sales on Binance Launchpad, and covering transaction fees on the BNB Chain.

Please note that cryptocurrency markets are highly volatile, and prices can change rapidly. For the most current information, it's advisable to consult reputable financial news sources or cryptocurrency exchanges.
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$SOL
101675412309634520Binance is one of the world's largest cryptocurrency exchanges, founded in 2017 by Changpeng Zhao (CZ). It offers a platform for trading hundreds of cryptocurrencies, including Bitcoin (BTC), Ethereum (ETH), and Binance Coin (BNB). Known for its low trading fees and high liquidity, Binance provides various financial services like spot and futures trading, staking, lending, and decentralized finance (DeFi) products.

Binance has its own blockchain, Binance Smart Chain (BSC), which supports smart contracts and decentralized applications (dApps). The platform also launched BNB, its native token, used for transaction fees, staking, and governance. Despite facing regulatory challenges in multiple countries, Binance continues expanding globally, adapting to compliance requirements. With innovations in Web3, NFTs, and metaverse projects, Binance remains a key player in the evolving crypto industry.
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Binance is one of the world's largest cryptocurrency exchanges, founded in 2017 by Changpeng Zhao (CZ). It offers a platform for trading hundreds of cryptocurrencies, including Bitcoin (BTC), Ethereum (ETH), and Binance Coin (BNB). Known for its low trading fees and high liquidity, Binance provides various financial services like spot and futures trading, staking, lending, and decentralized finance (DeFi) products.

Binance has its own blockchain, Binance Smart Chain (BSC), which supports smart contracts and decentralized applications (dApps). The platform also launched BNB, its native token, used for transaction fees, staking, and governance. Despite facing regulatory challenges in multiple countries, Binance continues expanding globally, adapting to compliance requirements. With innovations in Web3, NFTs, and metaverse projects, Binance remains a key player in the evolving crypto industry.
#VoteToDelistOnBinance Ethereum (ETH) is a decentralized, open-source blockchain that enables smart contracts and decentralized applications (dApps). Launched in 2015 by Vitalik Buterin and a team of developers, it introduced the concept of programmable blockchain technology. Unlike Bitcoin, which primarily serves as digital gold, Ethereum’s blockchain allows developers to build and execute applications using self-executing contracts. Ethereum transitioned from Proof of Work (PoW) to Proof of Stake (PoS) with the Ethereum 2.0 upgrade, improving scalability, security, and energy efficiency. Its native cryptocurrency, Ether (ETH), is used for transactions, staking, and paying gas fees. The Ethereum ecosystem powers decentralized finance (DeFi), non-fungible tokens (NFTs), and Web3 applications. With ongoing upgrades lik, Ethereum aims to enhance transaction speeds and reduce costs, solidifying its role in the future of decentralized computing.
#VoteToDelistOnBinance
Ethereum (ETH) is a decentralized, open-source blockchain that enables smart contracts and decentralized applications (dApps). Launched in 2015 by Vitalik Buterin and a team of developers, it introduced the concept of programmable blockchain technology. Unlike Bitcoin, which primarily serves as digital gold, Ethereum’s blockchain allows developers to build and execute applications using self-executing contracts.

Ethereum transitioned from Proof of Work (PoW) to Proof of Stake (PoS) with the Ethereum 2.0 upgrade, improving scalability, security, and energy efficiency. Its native cryptocurrency, Ether (ETH), is used for transactions, staking, and paying gas fees. The Ethereum ecosystem powers decentralized finance (DeFi), non-fungible tokens (NFTs), and Web3 applications. With ongoing upgrades lik, Ethereum aims to enhance transaction speeds and reduce costs, solidifying its role in the future of decentralized computing.
#TrumpAtDAS Binance is one of the world's largest cryptocurrency exchanges, founded in 2017 by Changpeng Zhao (CZ). It offers a platform for trading hundreds of cryptocurrencies, including Bitcoin (BTC), Ethereum (ETH), and Binance Coin (BNB). Known for its low trading fees and high liquidity, Binance provides various financial services like spot and futures trading, staking, lending, and decentralized finance (DeFi) products. Binance has its own blockchain, Binance Smart Chain (BSC), which supports smart contracts and decentralized applications (dApps). The platform also launched BNB, its native token, used for transaction fees, staking, and governance. Despite facing regulatory challenges in multiple countries, Binance continues expanding globally, adapting to compliance requirements. With innovations in Web3, NFTs, and metaverse projects, Binance remains a key player in the evolving crypto industry.
#TrumpAtDAS

Binance is one of the world's largest cryptocurrency exchanges, founded in 2017 by Changpeng Zhao (CZ). It offers a platform for trading hundreds of cryptocurrencies, including Bitcoin (BTC), Ethereum (ETH), and Binance Coin (BNB). Known for its low trading fees and high liquidity, Binance provides various financial services like spot and futures trading, staking, lending, and decentralized finance (DeFi) products.

Binance has its own blockchain, Binance Smart Chain (BSC), which supports smart contracts and decentralized applications (dApps). The platform also launched BNB, its native token, used for transaction fees, staking, and governance. Despite facing regulatory challenges in multiple countries, Binance continues expanding globally, adapting to compliance requirements. With innovations in Web3, NFTs, and metaverse projects, Binance remains a key player in the evolving crypto industry.
See my returns and portfolio breakdown. Follow for investment tips
See my returns and portfolio breakdown. Follow for investment tips
#ETHBreaks2k Binance is one of the world's largest cryptocurrency exchanges, founded in 2017 by Changpeng Zhao (CZ). It offers a platform for trading hundreds of cryptocurrencies, including Bitcoin (BTC), Ethereum (ETH), and Binance Coin (BNB). Known for its low trading fees and high liquidity, Binance provides various financial services like spot and futures trading, staking, lending, and decentralized finance (DeFi) products. Binance has its own blockchain, Binance Smart Chain (BSC), which supports smart contracts and decentralized applications (dApps). The platform also launched BNB, its native token, used for transaction fees, staking, and governance. Despite facing regulatory challenges in multiple countries, Binance continues expanding globally, adapting to compliance requirements. With innovations in Web3, NFTs, and metaverse projects, Binance remains a key player in the evolving crypto industry.
#ETHBreaks2k Binance is one of the world's largest cryptocurrency exchanges, founded in 2017 by Changpeng Zhao (CZ). It offers a platform for trading hundreds of cryptocurrencies, including Bitcoin (BTC), Ethereum (ETH), and Binance Coin (BNB). Known for its low trading fees and high liquidity, Binance provides various financial services like spot and futures trading, staking, lending, and decentralized finance (DeFi) products.

Binance has its own blockchain, Binance Smart Chain (BSC), which supports smart contracts and decentralized applications (dApps). The platform also launched BNB, its native token, used for transaction fees, staking, and governance. Despite facing regulatory challenges in multiple countries, Binance continues expanding globally, adapting to compliance requirements. With innovations in Web3, NFTs, and metaverse projects, Binance remains a key player in the evolving crypto industry.
#VoteToListOnBinance ne36812_.3ne36812_.3beginnerEthereum (ETH) is a decentralized, open-source blockchain that enables smart contracts and decentralized applications (dApps). Launched in 2015 by Vitalik Buterin and a team of developers, it introduced the concept of programmable blockchain technology. Unlike Bitcoin, which primarily serves as digital gold, Ethereum’s blockchain allows developers to build and execute applications using self-executing contracts. Ethereum transitioned from Proof of Work (PoW) to Proof of Stake (PoS) with the Ethereum 2.0 upgrade, improving scalability, security, and energy efficiency. Its native cryptocurrency, Ether (ETH), is used for transactions, staking, and paying gas fees. The Ethereum ecosystem powers decentralized finance (DeFi), non-fungible tokens (NFTs), and Web3 applications. With ongoing upgrades like sharding, Ethereum aims to enhance transaction speeds and reduce costs, solidifying its role in the future of decentralized computing.
#VoteToListOnBinance ne36812_.3ne36812_.3beginnerEthereum (ETH) is a decentralized, open-source blockchain that enables smart contracts and decentralized applications (dApps). Launched in 2015 by Vitalik Buterin and a team of developers, it introduced the concept of programmable blockchain technology. Unlike Bitcoin, which primarily serves as digital gold, Ethereum’s blockchain allows developers to build and execute applications using self-executing contracts.

Ethereum transitioned from Proof of Work (PoW) to Proof of Stake (PoS) with the Ethereum 2.0 upgrade, improving scalability, security, and energy efficiency. Its native cryptocurrency, Ether (ETH), is used for transactions, staking, and paying gas fees. The Ethereum ecosystem powers decentralized finance (DeFi), non-fungible tokens (NFTs), and Web3 applications. With ongoing upgrades like sharding, Ethereum aims to enhance transaction speeds and reduce costs, solidifying its role in the future of decentralized computing.
$ETH Ethereum (ETH) is a decentralized, open-source blockchain that enables smart contracts and decentralized applications (dApps). Launched in 2015 by Vitalik Buterin and a team of developers, it introduced the concept of programmable blockchain technology. Unlike Bitcoin, which primarily serves as digital gold, Ethereum’s blockchain allows developers to build and execute applications using self-executing contracts. Ethereum transitioned from Proof of Work (PoW) to Proof of Stake (PoS) with the Ethereum 2.0 upgrade, improving scalability, security, and energy efficiency. Its native cryptocurrency, Ether (ETH), is used for transactions, staking, and paying gas fees. The Ethereum ecosystem powers decentralized finance (DeFi), non-fungible tokens (NFTs), and Web3 applications. With ongoing upgrades like sharding, Ethereum aims to enhance transaction speeds and reduce costs, solidifying its role in the future of decentralized computing.
$ETH Ethereum (ETH) is a decentralized, open-source blockchain that enables smart contracts and decentralized applications (dApps). Launched in 2015 by Vitalik Buterin and a team of developers, it introduced the concept of programmable blockchain technology. Unlike Bitcoin, which primarily serves as digital gold, Ethereum’s blockchain allows developers to build and execute applications using self-executing contracts.

Ethereum transitioned from Proof of Work (PoW) to Proof of Stake (PoS) with the Ethereum 2.0 upgrade, improving scalability, security, and energy efficiency. Its native cryptocurrency, Ether (ETH), is used for transactions, staking, and paying gas fees. The Ethereum ecosystem powers decentralized finance (DeFi), non-fungible tokens (NFTs), and Web3 applications. With ongoing upgrades like sharding, Ethereum aims to enhance transaction speeds and reduce costs, solidifying its role in the future of decentralized computing.
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$BNB L0ET1689SHRDThis option needs to be tested. For option a, b, c, the values should be substituted into the equation to calculate the answer in the calculator, then the two values should be added and subtracted to see if they are equal. Similarly, the minimum value refers to the value that comes after solving the equation when substituted into that quantity. For example, here substituting the value of x into that equation yields 0, and that will be the answer.
$BNB
L0ET1689SHRDThis option needs to be tested. For option a, b, c, the values should be substituted into the equation to calculate the answer in the calculator, then the two values should be added and subtracted to see if they are equal. Similarly, the minimum value refers to the value that comes after solving the equation when substituted into that quantity. For example, here substituting the value of x into that equation yields 0, and that will be the answer.
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