Question

Find the value of k for which the following equation has equal roots. $x^2+4kx+(k^2-k+2)=0$.

Answer 1

For the given quadratic equation to have equal roots, its discriminant must be zero. i.e. $b^2-4ac=0$.

$\Rightarrow 16k^2-4(k^2-k+2)=0$

$\Rightarrow 12k^2+4k-8=0\Rightarrow 3k^2+k-2=0$

$\Rightarrow k=\frac{1}{3},-1$

Thus there are two values of $k$ for which the equation has equal roots and they are $\frac{1}{3}$ and $-1$ respectively.