Haryana Police Constable Model Paper 5

The form of roots of any quadratic equation $\left(\mathrm{a}{\mathrm{x}}^2+\mathrm{b}\mathrm{x}+\mathrm{c}\right)$ is determined from its discriminant,
$\mathrm{D}=\left({\mathrm{b}}^2-4\mathrm{ac}\right)$
For real and equal roots, the value of $\mathrm{D}=0$
For the given equation $\left({\mathrm{x}}^2-16\mathrm{x}+\mathrm{k}-4\right),$
$\mathrm{D}={16}^2-4\left(1\right)\left(\mathrm{k}-4\right)=0$
$\Rightarrow 256-4\mathrm{k}+16=0$
$\Rightarrow 4\mathrm{k}=256+16=272$
$\therefore \mathrm{k}=\frac{272}{4}=68$