Question:
Find the zeros of the quadratic polynomial $f(x)=4 \sqrt{3} x^{2}+5 x-2 \sqrt{3}$
Solution:
To find the zeros of the quadratic polynomial we will equate f(x) to 0
$\therefore f(x)=0$
$\Rightarrow 4 \sqrt{3} x^{2}+5 x-2 \sqrt{3}=0$
$\Rightarrow 4 \sqrt{3} x^{2}+8 x-3 x-2 \sqrt{3}=0$
$\Rightarrow 4 x(\sqrt{3} x+2)-\sqrt{3}(\sqrt{3} x+2)=0$
$\Rightarrow(\sqrt{3} x+2)(4 x-\sqrt{3})=0$
$\Rightarrow(\sqrt{3} x+2)=0$ or $(4 x-\sqrt{3})=0$
$\Rightarrow x=-\frac{2}{\sqrt{3}}$ or $x=\frac{\sqrt{3}}{4}$