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Write the Polynomial whose zeroes are $\sqrt{\frac{3}{2}}, -\sqrt{\frac{3}{2}}$.
Given: Zeroes of a polynomial are $\sqrt{\frac{3}{2}}, -\sqrt{\frac{3}{2}}$.
Solution:
Given Zeroes are $\sqrt{\frac{3}{2}}, -\sqrt{\frac{3}{2}}$
As Known if there are $\alpha$ and $\beta$, two zeroes of a polynomial, then the polynomial can be written as: $x-( \alpha+\beta)x+(\alpha\times\beta)=0$
Here $\alpha=\sqrt{\frac{3}{2}}\ and\ \beta=-\sqrt{\frac{3}{2}}$
Then the polynomial is:
$x^{2}-( \sqrt{\frac{3}{2}}-\sqrt{\frac{3}{2}})x+( \sqrt{\frac{3}{2}}\times\sqrt{\frac{3}{2}})=0$
$\Rightarrow x^{2}-( 0)x+\frac{3}{2}=0$
$\Rightarrow x^{2}+\frac{3}{2}=0$
$\Rightarrow \frac{2x^{2}+3}{2}=0$
$\Rightarrow 2x^{2}+3=0$
Thus, the polynomial is $2x^{2}+3=0$.
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