Question

Find the zeroes of the polynomial $5\sqrt{5}{x}^2+30x+8\sqrt{5}$.

• A. $\frac{-2}{\sqrt{5}}\text{and}\frac{-4}{\sqrt{5}}$
• B. $\frac{2}{\sqrt{5}}\text{and}\frac{4}{\sqrt{5}}$
• C. $\frac{2}{\sqrt{5}}\text{and}\frac{-4}{\sqrt{5}}$
• D. $\frac{-2}{\sqrt{5}}\text{and}\frac{4}{\sqrt{5}}$

Answer 1

The correct option is A $\frac{-2}{\sqrt{5}}\text{and}\frac{-4}{\sqrt{5}}$

By splitting the middle term, we get
$5\sqrt{5}{x}^2+30x+8\sqrt{5}=5\sqrt{5}{x}^2+20x+10x+8\sqrt{5}$
= $5x(\sqrt{5}x+4)+2\sqrt{5}(\sqrt{5}x+4)$
= $(5x+2\sqrt{5})(\sqrt{5}x+4)$
$⟹\text{Zeroes are}x=\frac{-2}{\sqrt{5}}\text{and}\frac{-4}{\sqrt{5}}$