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

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Solution

$p (x) = 3 x^{2} - 1$
So $3 x^{2} - 1 = 0$
$3 x^{2} = 1$
$\Rightarrow x^{2} = \frac{1}{3}$
$\Rightarrow x = \pm \frac{1}{\sqrt{3}}$
Roots $= \frac{1}{\sqrt{3}}, \frac{- 1}{\sqrt{3}}$ .

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Verify whether the following are zeroes of the polynomial, indicated against them.p(x)=3x2−1,x=−1√3,1√3

p(x)=3x2−1So 3x2−1=03x2=1⇒x2=13⇒x=±1√3Roots =1√3,−1√3.

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

$p (x) = 3 x^{2} - 1$
So $3 x^{2} - 1 = 0$
$3 x^{2} = 1$
$\Rightarrow x^{2} = \frac{1}{3}$
$\Rightarrow x = \pm \frac{1}{\sqrt{3}}$
Roots $= \frac{1}{\sqrt{3}}, \frac{- 1}{\sqrt{3}}$ .