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Find the Value of K for Which the Equation X2 + K(2x + K − 1) + 2 = 0 Has Real and Equal Roots. - Mathematics

Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.

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Solution

The given equation is x2+k(2x+k−1)+2=0.

⇒x2+2kx+k(k−1)+2=0

So, a = 1, b = 2k, c = k(k − 1) + 2

We know D=b2−4ac

⇒D=(2k)2 − 4 × 1 × [k(k − 1) + 2]

⇒D=4k− 4[k− k + 2]

⇒D=4k− 4k+ 4k − 8

⇒D=4k − 8 = 4(k − 2)

For equal roots, D = 0

Thus, 4(k − 2) = 0

So, k = 2.

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