Question

What are the values of k when kx2+x+k, has equal zeroes?

Answer 1

Given the equation $kx^2+x+k=0$. When this quadratic equation has equal roots,

The discriminant should be 0. For the equation $ax^2+bx+c=0$, the discriminant is $b^2-4ac$. Since for the given equation discriminant is 0, we have

$1^2-4k^2=0\\ 4k^2=1\\ k=\pm \frac{1}{2}$