Question

Solve the following quadratic equation by factorization,
$3\sqrt{5}{x}^2+25x-10\sqrt{5}=0$ the roots are

• A. $\frac{\sqrt{5}}{2}$ $,-2\sqrt{5}$
• B. $\frac{\sqrt{5}}{3}$ $,-2\sqrt{5}$
• C. $\frac{\sqrt{5}}{5}$ $,-2\sqrt{5}$
• D. $\frac{\sqrt{5}}{2}$ $,-2\sqrt{2}$

Answer 1

The correct option is B $\frac{\sqrt{5}}{3}$ $,-2\sqrt{5}$

$3\sqrt{5}{x}^2+25x-10\sqrt{5}=0$

$\Rightarrow$ $3\sqrt{5}{x}^2+30x-5x-10\sqrt{5}=0$

$\Rightarrow$ $3x(\sqrt{5}x+10)-\sqrt{5}(\sqrt{5}x+10)=0$

$\Rightarrow$ $(\sqrt{5}x+10)(3x-\sqrt{5})=0$

$\Rightarrow$ $\sqrt{5}x+10=0$ and $3x-\sqrt{5}=0$

$\Rightarrow$ $x=\frac{-10}{\sqrt{5}}$ and $x=\frac{\sqrt{5}}{3}$

$\Rightarrow$ $x=\frac{-2\times \sqrt{5}\times \sqrt{5}}{\sqrt{5}}$ and $x=\frac{\sqrt{5}}{3}$

$\therefore$ $x=-2\sqrt{5}$ and $x=\frac{\sqrt{5}}{3}$