Question

Find the roots of the equation $8+6p-\frac{1}{2}{p}^2=0$

Answer 1

$8+6p-\frac{1}{2}{p}^2=0$

$\Rightarrow -p^2+12p+16=0$

$\Rightarrow p^2-12p-16=0$

$\Rightarrow p^2-2\times 6p+36-36-16=0$

$\Rightarrow {(p-6)}^2-52=0$

$\Rightarrow p-6=\pm \sqrt{52}=\pm 2\sqrt{13}$

$\therefore p=6\pm 2\sqrt{13}$

$\therefore p=6+2\sqrt{13},6-2\sqrt{13}$