Find the zeroes of the polynomial 3x2-2 and verify the relationship between the zeroes and coefficients.

Given,
Quadratic equation is,

3 x^{2} - 2

= 0

x^{2} = \frac{2}{3}

Take square root both side,

x = \pm \sqrt{\frac{2}{3}}

So, the roots are,

\sqrt{\frac{2}{3}}

and

- \sqrt{\frac{2}{3}}

Now, sum of the roots of quadratic equation

= \frac{- (coefficient of x)}{coefficient of x^{2}}

= \frac{- 0}{3}

= 0

.
Product of the roots of quadratic equation

= \frac{constant term}{coefficient of x^{2}}

= \frac{- 2}{3}

.
Now, the sum of roots which we have obtained,

\sqrt{\frac{2}{3}} - \sqrt{\frac{2}{3}} = 0

Product of roots,

\sqrt{\frac{2}{3}} \times (- \sqrt{\frac{2}{3}}) = - \frac{2}{3}

So, we have verified the given condition.
So, the roots of the given equation are,

\sqrt{\frac{2}{3}}

and

- \sqrt{\frac{2}{3}}

Hence, option 3 is correct.

Find the zeroes of the polynomial $3 x^{2} - 2$ and verify the relationship between the zeroes and coefficients.