Question

Determine the values of $p$ for which the quadratic equation $2x^2+px+8=0$ has equal roots.

• A. $p=\pm 64$
• B. $p=\pm 8$
• C. $p=\pm 4$
• D. $p=\pm 16$

Answer 1

Answer: (B)

$p=\pm 8$

In $a{x}^2+bx+c=0,$
Discriminant $D$ $=b^2-4ac$,
D$=0$, for the roots to be real and equal

In $2x^2+px+8=0$

Thus, we have $a=2,b=p$ and $c=8$

Then $D$ $=b^2-4ac=0$

$\therefore p^2-4\times 2\times 8=0\Rightarrow p^2-64=0$

$\Rightarrow p=\pm 8$.