Question

Find the value of k so that the quadratic equation x2+4kx+(k^2-k+2)=0 has equal roots.

Answer 1

Concept used :-

If A•x^2 + B•x + C = 0 ,is any quadratic equation,

then its discriminant is given by;

D = B^2 - 4•A•C

• If D = 0 , then the given quadratic equation has real and equal roots.

• If D > 0 , then the given quadratic equation has real and distinct roots.

• If D < 0 , then the given quadratic equation has unreal (imaginary) roots...

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Solution :-

Comparing The Given Quadratic Equation x²+4kx+(k^2-k+2) = 0 with A•x^2 + B•x + C = 0 we get,

➻ A = 1

➻ B = 4k

➻ C = (k² - k + 2)

Since Roots Are Equal , So, D = 0

➪ B^2 - 4•A•C = 0

➪ (4k)² - 4*1*(k² - k + 2) = 0

➪ 16k² - 4k² + 4k - 8 = 0

➪ 12k² + 4k - 8 = 0

➪ 12k² + 12k - 8k - 8 = 0

➪ 12k(k + 1) - 8(k + 1) = 0

➪ (k + 1)(12k - 8) = 0

Putting Both Equal to Zero,

➪ k+1 = 0

➪ k = (-1).

Or,

➪ 12k - 8 = 0

➪ 12k = 8

➪ k = (8/12)

➪ k = (2/3).

Hence, k € { (-1) , (2/3) }.

Answer 2

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