Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases:$ g(x)=3 x^{2}-2, x=\frac{2}{\sqrt{3}},-\frac{2}{\sqrt{3}} $
Given:
\( g(x)=3 x^{2}-2, x=\frac{2}{\sqrt{3}},-\frac{2}{\sqrt{3}} \)
To do:
We have to find whether the indicated numbers are zeros of the polynomials corresponding to them.
Solution:
To find whether $x=\frac{2}{\sqrt{3}},-\frac{2}{\sqrt{3}}$ are zeroes of $g(x)$ we have to check if $g(\frac{2}{\sqrt{3}})=0$ and $g(-\frac{2}{\sqrt{3}})=0$.
Therefore,
$g(\frac{2}{\sqrt{3}})=3(\frac{2}{\sqrt{3}})^{2}-2$
$=3 \times \frac{4}{3}-2$
$=4-2$
$=2$
$g(\frac{-2}{\sqrt{3}})=3(\frac{-2}{\sqrt{3}})^{2}-2$
$=3 \times \frac{4}{3}-2$
$=4-2$
$=2$
Therefore, $x=\frac{2}{\sqrt{3}}$ and $x=\frac{2}{\sqrt{3}}$ are not zeroes of $g(x)$.
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