Question

Find the value of k for which each of the following quadratic equation has equal roots.

(k-4)x^{​​​​​​2} +2(k-4)x +4=0.

Answer 1

For equal roots, b^2 - 4ac = 0

Here, a = k - 4, b = 2k - 8, c = 4

So, b^2 - 4ac = 0 shows that,

{2k - 8}^2 - 4*{k - 4}*4 = 0

ie, 4k^2 - 32k + 64 - 16{k - 4} = 0

ie, 4k^2 - 32k + 64 - 16k + 64 = 0

ie, 4k^2 - 48k + 128 = 0

ie, k^2 - 12k + 32 = 0

ie,(k-8)(k-4)=0
so we can say that

k = 8, 4