Write the zeros of the quadratic polynomial f(x)

To find the zeros of the quadratic polynomial we will equate f(x) to 0

$\therefore f(x)=0$

$\Rightarrow 6 x^{2}-3=0$

$\Rightarrow 3\left(2 x^{2}-1\right)=0$

$\Rightarrow 2 x^{2}-1=0$

$\Rightarrow 2 x^{2}=1$

$\Rightarrow x^{2}=\frac{1}{2}$

$\Rightarrow x=\pm \frac{1}{\sqrt{2}}$

Hence, the zeros of the quadratic polynomial $f(x)=6 x^{2}-3$ are $\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}$.