Question

State whether True or False, if the following are zeros of the polynomial, indicated against them:

$p\left(x\right)=3x^2-1,x=-\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$.

• A. True
• B. False

Answer 1

The correct option is A True

The given polynomial is $p\left(x\right)=3x^2-1$.

We find the zeros of the polynomial by equating the polynomial $p\left(x\right)$ to zero as shown below:

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

Hence, the zeroes of the polynomial $p\left(x\right)=3x^2-1$ are $x=-\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$.

Therefore, it is true and option $A$ is correct.