Question

On solving the following quadratic equation by factorization, the roots are $\frac{\sqrt{3}}{4},-\frac{2}{\sqrt{3}}$
$4\sqrt{3}{x}^2+5x-2\sqrt{3}=0$

• A. True
• B. False

Answer 1

The correct option is A True

$4\sqrt{3}{x}^2+5x-2\sqrt{3}=0$

$\Rightarrow$ $4\sqrt{3}{x}^2+8x-3x-2\sqrt{3}=0$

$\Rightarrow$ $4x(\sqrt{3}x+2)-\sqrt{3}(\sqrt{3}x+2)=0$

$\Rightarrow$ $(\sqrt{3}x+2)(4x-\sqrt{3})=0$

$\Rightarrow$ $\sqrt{3}x+2=0$ and $4x-\sqrt{3}=0$

$\Rightarrow$ $x=-\frac{2}{\sqrt{3}}$ and $x=\frac{\sqrt{3}}{4}$

$\therefore$ $\frac{\sqrt{3}}{4},-\frac{2}{\sqrt{3}}$ are root of the given quadratic equation $4\sqrt{3}{x}^2+5x-2\sqrt{3}=0$ is true.