Question

Find the zeroes of the quadratic polynomial 3x^2 − 2 and verify the relationship between the zeroes and the coefficients.

Please it's very urgent

Answer 1

Answer :-

Given Polynomial :-

3x² - 2

Finding zeros :-

As it is in the form of

a² - b²

Factorisation = (a + b)(a - b)

$= (\sqrt{3}x + \sqrt{2}) ( \sqrt{3}x - \sqrt{2})$

Zeros

$= \dfrac{-\sqrt{2}}{\sqrt{3}} \: and \: \dfrac{\sqrt{2}}{\sqrt{3}}$

Now as

Sum of roots = -b/a

$\implies\dfrac{0}{3} = \dfrac{-\sqrt{2}}{\sqrt{3}} \: +\: \dfrac{\sqrt{2}}{\sqrt{3}}$

$\implies\dfrac{0}{3} = \dfrac{-\sqrt{2} + \sqrt{2}}{\sqrt{3}}$

$\implies\dfrac{0}{3} = \dfrac{-\sqrt{0}}{\sqrt{3}}$

Hence sum of roots verified

Product of zeros = c/a

$\implies\dfrac{-2}{3} = \dfrac{-\sqrt{2}}{\sqrt{3}} \times \dfrac{\sqrt{2}}{\sqrt{3}}$

$\implies\dfrac{-2}{3} = \dfrac{-\sqrt{2}^2}{\sqrt{3}^2}$

$\implies\dfrac{-2}{3} = \dfrac{-2}{3}$

Hence product of roots verified