Question

Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases:

(iii) $f\left(x\right)=3x^2-2,$
$x=\frac{2}{\sqrt{3}},-\frac{2}{\sqrt{3}}$

Answer 1

Given : $f\left(x\right)=3x^2-2andx=\frac{2}{\sqrt{3}},-\frac{2}{\sqrt{3}}$

We know that if $f\left(a\right)=0;$ then $a$ is the zero of the polynomial $f\left(x\right).$

$\therefore f\left(\frac{2}{\sqrt{3}}\right)=3\times {\left(\frac{2}{\sqrt{3}}\right)}^2-2$

$=3\times \frac{4}{3}-1=3$

And $f(-\frac{2}{\sqrt{3}})=3\times {(-\frac{2}{\sqrt{3}})}^2-2$

$=3\times \frac{4}{3}-1=3$

$\because f\left(\frac{2}{\sqrt{3}}\right)\ne 0andf(-\frac{2}{\sqrt{3}})\ne 0$

Hence, $x=\frac{2}{\sqrt{3}}-\frac{2}{\sqrt{3}}$ is not the zero of $f\left(x\right)=3x^2-2,$ verified.