Question
Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:$\text{g(x)}=3\text{x}^2-2,\text{x}=\frac{2}{\sqrt{3}},\frac{-2}{\sqrt{3}}$
✓
Answer
$\text{g(x)}=3\text{x}^2-2,\text{x}=\frac{2}{\sqrt{3}},\frac{-2}{\sqrt{3}}$We know that
$\text{g(x)}=3\text{x}^2-2$
Given that,
$\text{x}=\Big(\frac{2}{\sqrt{3}},\frac{-2}{\sqrt{3}}\Big)$
Substitute $\text{x}=\frac{2}{\sqrt{3}}$ in g(x)
$\text{g}\Big(\frac{2}{\sqrt{3}}\Big)=3\Big(\frac{2}{\sqrt{3}}\Big)^2-2$
$=3\Big(\frac{4}{3}\Big)-2$
$=4-2$
$=2\neq0$
Now, Substitute $\text{x}=-\frac{2}{\sqrt{3}}$ in g(x)
$\text{g}\Big(\frac{-2}{\sqrt{3}}\Big)=3\Big(\frac{-2}{\sqrt{3}}\Big)^2-2$
$=3\Big(\frac{4}{3}\Big)-2$
$=4-2$
$=2\neq0$
Since, the results when
$\text{x}=\Big(\frac{2}{\sqrt{3}},\frac{-2}{\sqrt{3}}\Big)$ are not 0, they are roots of $3x^2 - 2$
$\text{g(x)}=3\text{x}^2-2$
Given that,
$\text{x}=\Big(\frac{2}{\sqrt{3}},\frac{-2}{\sqrt{3}}\Big)$
Substitute $\text{x}=\frac{2}{\sqrt{3}}$ in g(x)
$\text{g}\Big(\frac{2}{\sqrt{3}}\Big)=3\Big(\frac{2}{\sqrt{3}}\Big)^2-2$
$=3\Big(\frac{4}{3}\Big)-2$
$=4-2$
$=2\neq0$
Now, Substitute $\text{x}=-\frac{2}{\sqrt{3}}$ in g(x)
$\text{g}\Big(\frac{-2}{\sqrt{3}}\Big)=3\Big(\frac{-2}{\sqrt{3}}\Big)^2-2$
$=3\Big(\frac{4}{3}\Big)-2$
$=4-2$
$=2\neq0$
Since, the results when
$\text{x}=\Big(\frac{2}{\sqrt{3}},\frac{-2}{\sqrt{3}}\Big)$ are not 0, they are roots of $3x^2 - 2$
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