Question

If x² + k (4x + k -1) +2 =0 has equal roots, then find the value of k?​

Answer 1

Answer:

Given equation is -

$x² + k (4x + k -1) +2 =0$

$=> x²+ 4kx+ k²- k+2 = 0$

Here,

$a = 1 \\ b = 4k \\ and \: c = {k}^{2} - k + 2$

For real and equal roots ,

$D=0$

$D = \sqrt{b²-4ac}$

$= > \sqrt{ (4k)²-4(1)(k²-k+2)} = 0$

$= > 16k²-4(k²-k+2)=0$

$= > 4k²-k²+k-2=0$

$= > 3k²+k-2=0$

$= > 3k²+3k-2k-2=0$

$= > 3k(k+1)-2(k+1)=0$

$= > (3k-2)(k+1)=0$

$So, k = \frac{2}{3} \: or \: k = -1$