Question

Find the values of $k$ for which the given equation has real and equal roots
$k{x}^2-5x+k=0$

Answer 1

The given equation is $k{x}^2-5x+k=0$

Here $a=k,b=-5,c=k$

$\therefore D=b^2-4ac={(-5)}^2-4\times k\times \left(k\right)=25-4k^2$

The given equation will have real and equal roots if

$D=0\Rightarrow 25-4k^2=0\Rightarrow k=\pm \frac{5}{2}$