Question

Solve the following quadratic equation by factorization method: $\sqrt{5}{x}^2+2x-3\sqrt{5}=0$

• A. $\{-\sqrt{5},\frac{3}{\sqrt{5}}\}$
• B. $\{\sqrt{5},\frac{3}{\sqrt{5}}\}$
• C. $\{-\sqrt{5},\frac{-3}{\sqrt{5}}\}$
• D. None of these

Answer 1

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

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

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

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

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

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

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