Question

x^2+k(4x+k-1)+2-0 has equal roots then k=​

Answer 1

The given quadratic equation has two equal roots.

So, Discriminant = $b^2 - 4ac = 0$

$x^2+k(4x+k-1)+2-0 = 0$  

$x^2 + 4kx+ k^2 - k + 2 = 0$ ..............................(1)

By comparing (1) with the general form of quadratic equation:

a = 1

b = 4$k$

c = $k^2 -k + 2$

$b^2 - 4ac = 0$

$(4k)^2 - 4(1)(k^2 - k + 2) = 0\\16k^2 - 4k^2 + k - 2 = 0\\12k^2 + k - 2 = 0\\k = \frac{-1 + \sqrt{97}}{24} (0r) \frac{-1 - \sqrt{97}}{24}$