Question

Find such value of $k$ for quotation equation $k{x}^2-2kx+6=0$ so that they have two equal roots.

Answer 1

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

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

For equal roots,

$D=0$

$b^2-4ac=0$

${(-2k)}^2-4\left(k\right)\left(6\right)=0$

$4k^2-24k=0$

$4k(k-6)=0$

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

Hence the value of $k$ is $0$ or $6$.