Question

Find the value of $k$ for which the given equation has equal roots. Also, find the roots.
$2k{x}^2-40x+25=0$

Answer 1

The given equation is $2k{x}^2-40x+25=0$

Here, $a=2k,b=-40,c=25$

$\therefore D=b^2-4ac={(-40)}^2-4\times 2k\times 25=1600-200k$

The equation will have equal roots, if $D=0$$\Rightarrow 1600-200k=0$

$\Rightarrow k=8$

Substituting $k=8$ in the given equation, we get

$16x^2-40x+25=0\Rightarrow {(4x-5)}^2=0\Rightarrow x=\frac{5}{4}$

Hence, the roots of the given equation are each equal to $\frac{5}{4}$