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# Verify whether the following are zeroes of the polynomial, indicated against it. (vii) p(x) = 3 x ^2 - 1, x = - 1 / root 3, 2 / root 3

3.(vii)  Verify whether the following are zeroes of the polynomial, indicated against it.

(vii)    $p(x) = 3x^2 - 1, \ x = -\frac{1}{\sqrt3}, \frac{2}{\sqrt3}$

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Given polynomial is   $p(x) = 3x^2-1$

Now, at  $x = -\frac{1}{\sqrt3}$   it's value is

$p\left ( -\frac{1}{\sqrt3} \right )= 3 \times \left ( -\frac{1}{\sqrt3} \right )^2-1 = 1-1 =0$

And at  $x = \frac{2}{\sqrt3}$

$p\left ( \frac{2}{\sqrt3} \right )= 3 \times \left ( \frac{2}{\sqrt3} \right )^2-1 = 4-1 =3\neq 0$

Therefore,   $x = -\frac{1}{\sqrt3}$  is a zeros of polynomial$p(x) = 3x^2-1$

whereas $x = \frac{2}{\sqrt3}$  is not a zeros of  polynomial $p(x) = 3x^2-1$

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