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}

Answers (1)

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 polynomialp(x) = 3x^2-1

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

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