Question

If the quadratic equation $k{x}^2-2kx+6=0$ has equal roots, then find the value of $k$.

Answer 1

Quadratic equation has equal roots then $b^2-4ac=0$

Given that $k{x}^2-2kx+6=0$

Here $a=k,b=-2k$ and $c=6$

Now, ${(-2k)}^2-4\times k\times 6=0$

$\Rightarrow 4k^2-24k=0$

$\Rightarrow 4k(k-6)=0$

$\Rightarrow k=0$ or $k=6$