Write the Polynomial whose zeroes are $\sqrt{\frac{3}{2}}, -\sqrt{\frac{3}{2}}$.

Given: Zeroes of a polynomial are $\sqrt{\frac{3}{2}}, -\sqrt{\frac{3}{2}}$.

 To do: To write the polynomial with the given zeroes.

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 $2x^{2}+3=0$.