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

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Solution

$3 x^{2} - 2 = 0 x^{2} = \frac{2}{3} x = \pm \sqrt{\frac{2}{3}}$
Sum of roots $= - \frac{b}{a} = \frac{0}{3} = 0$
$\sqrt{\frac{2}{3}} + (- \sqrt{\frac{2}{3}}) = 0$
Product of roots $= \frac{c}{a} = \frac{- 2}{3}$
Product $\sqrt{\frac{2}{3}} \times (- \sqrt{\frac{2}{3}}) = - \frac{2}{3}$

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