Question

Find the value of P for which the following equation has equal roots ${px}^2-8x+2p=0$

• A. $\pm 2\sqrt{2}$
• B. $\pm \sqrt{2}$
• C. $\pm \sqrt{3}$
• D. $\pm 2\sqrt{3}$

Answer 1

Answer: (A)

$\pm 2\sqrt{2}$

Given equation is: ${px}^2-8x+2p=0$
Here, $a=p,b=-8,c=2p$
For equal roots $b^2-4ac=0$
$\therefore {(-8)}^2-4\left(p\right)\left(2p\right)=0$
$64-8p^2=0$
$-8p^2=-64$
$8p^2=64$
$p^2=\frac{64}{8}=8$
$\therefore p=\pm \sqrt{8}=\pm 2\sqrt{2}$