Question

Determine $k$ for which the quadratic equation has equal roots $k{x}^2-5x+k=0$.

Answer 1

The given equation is,

$k{x}^2-5x+k=0$

The roots of the quadratic equation $A{x}^2+Bx+C=0$ are

$x=\frac{-B\pm \sqrt{B^2-4AC}}{2A}$

So, the equation has equal roots if $B^2-4AC=0$

for the given equation,

$B^2-4AC=(-5{)}^2-4(k\left)\right(k)=0$

$25-4k^2=0$

$k^2=\frac{25}{4}$

$k=\pm \frac{5}{2}$