Question

find the zeroes of the quadratic polynomial 3x^2-2 and verify the relation ship between the zeroes and the coefficient​

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

3x² - 2 = 0

Arrange it in formula we get :-

(√3x)² - √2² =0

★Identity :- a² - b² = (a + b)(a - b)

(√3x -√2 )(√3x+√2) =0

$\tt{\rightarrow x=\dfrac{\sqrt{2}}{\sqrt{3}}}$

$\tt{\rightarrow x=\dfrac{-\sqrt{2}}{\sqrt{3}}}$

★Verification :-

$\tt{\rightarrow Sum\;of\;zero=\dfrac{-b}{a}}$

${\rightarrow x=\dfrac{\sqrt{2}}{\sqrt{3}}-\dfrac{\sqrt{2}}{\sqrt{3}}}$

0 = 0

$\tt{\rightarrow Product\;of\;zero=\dfrac{-b}{a}}$

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

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

${\boxed{\bigstar{{Hence\;we\;get\;verified}}}}$

Answer 2

. Solution .

3x ^2 - 2 = 0

3x ^2 = 2

x^2 = 2/3

So X = √2 /√3 or - √2 / √3

So now , verify the relation ship between the zeroes and the coefficient .

The sum of the zeroes = - b/a

= √ 2 /√3 - √2 /√3 = 0

0 = 0

The product of zeroes = c/a

= √2 / √3 × -√ 2 / √ 3 = - 2 / 3

= - 2 / 3 = - 2 / 3

= So It get verified .