Question

For what value of $k$, the equation $k{x}^2-6x-2=0$ has equal roots.

Answer 1

The condition for a quadratic equation $a{x}^2+bx+c=0$ to have equal roots, is

$b^2-4ac=0$

For the given equation $k{x}^2-6x-2=0$

$b^2-4ac=(-6{)}^2-4k(-2)=0$

$36+8k=0$

$8k=-36$

$k=-\frac{36}{8}=-\frac{9}{2}$