Verify whether the following are zeroes of the polynomial indicated against them:
$p(x) = 3x^2 - 1, x = -\frac{1}{\sqrt{3}}, \frac{2}{\sqrt{3}}$

(N/A) To verify if the given values are zeroes of the polynomial $p(x) = 3x^2 - 1$,we substitute the values of $x$ into the polynomial. If the result is $0$,then the value is a zero of the polynomial.
Step $1$: Check for $x = -\frac{1}{\sqrt{3}}$:
$p\left(-\frac{1}{\sqrt{3}}\right) = 3\left(-\frac{1}{\sqrt{3}}\right)^2 - 1$
$= 3\left(\frac{1}{3}\right) - 1$
$= 1 - 1 = 0$
Since $p\left(-\frac{1}{\sqrt{3}}\right) = 0$,$x = -\frac{1}{\sqrt{3}}$ is a zero of the polynomial.
Step $2$: Check for $x = \frac{2}{\sqrt{3}}$:
$p\left(\frac{2}{\sqrt{3}}\right) = 3\left(\frac{2}{\sqrt{3}}\right)^2 - 1$
$= 3\left(\frac{4}{3}\right) - 1$
$= 4 - 1 = 3$
Since $p\left(\frac{2}{\sqrt{3}}\right) \neq 0$,$x = \frac{2}{\sqrt{3}}$ is not a zero of the polynomial.