Find the value(s) of `k` so that, the quadratic equation `x^2 - 4kx + k = 0` has equal roots.

Answer

`k=0" or "k=(1)/(4)`

Explanation

`D=(-4k)^(2)-4l=16k^(2)-4k=4k(4k-1).`
For equal roots, we must have D = 0.
Now, `D=0implies4k(4k-1)=0impliesk=0" or "4k-1=0impliesk=0" or "k=(1)/(4).`