Question

Find the value of k for

which the following quadratic

equation has real and equal

roots :x2 +k(2x+k- 1)=0.​

Answer 1

Ur Equations is incomplete !!

It should be x²+k(2x+k−1)+2=0.

instead of x² +k(2x+k- 1)=0.

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=4k² − 4[k² − k + 2]

⇒D=4k² − 4k² + 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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