Question

The zeroes of the polynomial p(x) = 3x² − 1 are
(a) $\frac{1}{3}$
(b) $\frac{1}{\sqrt{3}}$
(c) $\frac{-1}{\sqrt{3}}$
(d) $\frac{1}{\sqrt{3}}\mathrm{and}\frac{-1}{\sqrt{3}}$

Answer 1

(d) $\frac{1}{\sqrt{3}}\mathrm{and}\frac{-1}{\sqrt{3}}$

Let:
$p\left(x\right)=3x^2-1$

$$\begin{gathered} \mathrm{To}\mathrm{find}\mathrm{the}\mathrm{zeroes}\mathrm{of}\mathrm{p}\left(\mathrm{x}\right),\mathrm{we}\mathrm{have}: \\ p\left(x\right)=0\Rightarrow 3x^2-1=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow 3x^2=1 \\ \Rightarrow x^2=\frac{1}{3} \\ \Rightarrow x=\pm \frac{1}{\sqrt{3}} \\ \Rightarrow x=\frac{1}{\sqrt{3}}\text{and}x=-\frac{1}{\sqrt{3}} \end{gathered}$$