Question

Find the value(s) of k so that the quadratic equation x² − 4kx + k = 0 has equal roots.

Answer 1

Given equation is x² − 4kx + k = 0

For the given equation to have equal roots, D = 0.

`rArr b^2-4ac=0 `

`rArr (-4k)^2-4(1)(k)=0`

`rArr  16k^2-4k=0`

`rArr 4k(4k-1)=0`

`rArr4k=0`or `k=1/4`

Hence, for k = 0 or `1/4`, the given equation will have equal roots.