Math, asked by WyldeGirl, 2 months ago

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

Answers

Answered by Ʀíɗɗℓεʀ
370

Corrected Question :

  • Find the value of k for which the quadratic equation x² - 2(2k - 1)x + 4 = 0 her real and equal roots.

~Answer :

  • The value of k = 1/4

______________

Solution : The given quadratic equation is,

  • x² - 2(2k - 1)x + 4 = 0.

~

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

~

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

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

  • \boxed{\sf{\pmb{\purple{c~=~4}}}}

~

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

~

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}}}}}

~

Hence,

  • The value of k = 1/4.

Aryan0123: Awesome! Keep it up.
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