Question

➛Quᥱ᥉tioꪀ
$x {}^{2} - (2k + 1)x + 4 = 0$
Answer Correctly :)~​

Answer 1

Corrected Question :

• Find the value of k for which the quadratic equation k²x² - 2(2k - 1)x + 4 = 0 her real and equal roots.

~Answer :

• The value of k = 1/4

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Solution : The given quadratic equation is,

• k²x² - 2(2k - 1)x + 4 = 0.

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• Comparing the given quadratic equation with the general quadratic equation ax² + bx + c = 0 ;

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${\sf:\implies{a~=~x^2}}$

${\sf:\implies{b~=~- 2(2k~-~1)}}$

• $\boxed{\sf{\pmb{\purple{c~=~4}}}}$★

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• Real and equal roots , it's discriminant must be zero.

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Therefore,

${\sf:\implies{D~=~0}}$

${\sf:\implies{b^2~-~4ac~=~0}}$

${\sf:\implies{[ - 2(2k~-~1)]^2~-~4•k^2•4~=~0}}$

${\sf:\implies{4(4k^2~+~1~-~4k)~-~4•4k^2~=~0}}$

${\sf:\implies{4(4k^2~+~1~-~4k^2)~=~0}}$

${\sf:\implies{1~-~4k~=~0}}$

${\sf:\implies{4k~=~1}}$

• $\boxed{\sf{\pmb{\pink{k~=~\dfrac{1}{4}}}}}$★

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Hence,

• The value of k = 1/4.