Question

Find the roots of the following quadratic equation

$4p^2+7=12p$

• A. $p=\frac{5\pm \sqrt{2}}{2}$
• B. $p=\frac{4\pm \sqrt{2}}{2}$
• C. $p=\frac{3\pm \sqrt{2}}{2}$
• D. $p=\frac{2\pm \sqrt{2}}{2}$

Answer 1

The correct option is C $p=\frac{3\pm \sqrt{2}}{2}$

Given equation is

$4p^2+7=12p$
$4p^2-12p+7=0$
$a=4,b=-12,c=7$

$p=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
$p=\frac{12\pm \sqrt{144-4\left(4\right)\left(7\right)}}{2\times 4}$
$p=\frac{12\pm \sqrt{32}}{8}$
$\therefore p=\frac{3\pm \sqrt{2}}{2}$

$\therefore$ the roots of the given equation are $\frac{3\pm \sqrt{2}}{2}$