Question

If the following quadratic equation has two equal and real roots then find the value of $k:$
$5x^2-2kx+20=0$

Answer 1

If a quadratic equation has real and equal roots then its discriminant is equal to zero. So,

$D=0$

$\Rightarrow D=4k^2-4\left(20\right)\left(5\right)$

$\Rightarrow k^2-100=0$

$\Rightarrow (k+10)(k-10)=0$

$\Rightarrow k=10,-10$