Question

Find the zeros of the quadratic polynomial $f\left(x\right)=4\sqrt{3}{x}^2+5x-2\sqrt{3}$

Answer 1

To find the zeros of the quadratic polynomial we will equate f(x) to 0
$$\begin{gathered} \therefore f\left(x\right)=0 \\ \Rightarrow 4\sqrt{3}{x}^2+5x-2\sqrt{3}=0 \\ \Rightarrow 4\sqrt{3}{x}^2+8x-3x-2\sqrt{3}=0 \\ \Rightarrow 4x\left(\sqrt{3}x+2\right)-\sqrt{3}\left(\sqrt{3}x+2\right)=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow \left(\sqrt{3}x+2\right)\left(4x-\sqrt{3}\right)=0 \\ \Rightarrow \left(\sqrt{3}x+2\right)=0\mathrm{or}\left(4x-\sqrt{3}\right)=0 \\ \Rightarrow x=-\frac{2}{\sqrt{3}}\mathrm{or}x=\frac{\sqrt{3}}{4} \end{gathered}$$
Hence, the zeros of the quadratic polynomial $f\left(x\right)=4\sqrt{3}{x}^2+5x-2\sqrt{3}$ are $-\frac{2}{\sqrt{3}}\mathrm{or}\frac{\sqrt{3}}{4}$.