Question

Find the zeroes of the quadratic polynomial ${\displaystyle f\left(x\right)=4\sqrt{3}{x}^2+5x–2\sqrt{3}}$.

Answer 1

To find the zeroes of the quadratic polynomial we will equate f(x) to 0
∴f(x) = 0
${\displaystyle \Rightarrow 4\sqrt{3}{x}^2+5x–2\sqrt{3}=0}$
${\displaystyle \Rightarrow 4\sqrt{3}x2+8x–3x–2\sqrt{3}=0}$
${\displaystyle \Rightarrow 4x(\sqrt{3}x+2)–\sqrt{3}(\sqrt{3}x+2)=0}$
${\displaystyle \Rightarrow (\sqrt{3}x+2)=0\text{or}(4x–\sqrt{3})=0}$ 

${\displaystyle \Rightarrow x=-\frac{2}{\sqrt{3}}\text{or}x=\frac{\sqrt{3}}{4}}$ 

Hence, the zeroes of the quadratic polynomial${\displaystyle f\left(x\right)=4\sqrt{3}{x}^2+5x-2\sqrt{3} are-\frac{2}{\sqrt{3}}\text{or}\frac{\sqrt{3}}{4}}$