Question

Solve the following equation by factorisation :

${\displaystyle \sqrt{3}{x}^2+10x+7\sqrt{3}}$ = 0

Answer 1

${\displaystyle \sqrt{3}{x}^2+10x+7\sqrt{3}}$ = 0
⇒ ${\displaystyle \sqrt{3}{x}^2+3x+7x+7\sqrt{3}}$ = 0
⇒ ${\displaystyle \sqrt{3}x(x+\sqrt{3})+7(x+\sqrt{3})}$ = 0
⇒ ${\displaystyle (x+\sqrt{3})(\sqrt{3}+7)}$ = 0
Either ${\displaystyle x+\sqrt{3}}$ = 0,
then x = ${\displaystyle -\sqrt{3}}$
or
${\displaystyle \sqrt{3}x+7}$ = 0,
then ${\displaystyle \sqrt{3}x}$ = –7

⇒ x = ${\displaystyle \frac{-7}{\sqrt{3}}}$

x = ${\displaystyle \frac{-7\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}}$

= ${\displaystyle \frac{-7\sqrt{3}}{3}}$

Hence x = ${\displaystyle -\sqrt{3},\frac{-7\sqrt{3}}{3}}$.