Find a quadratic polynomial , the sum and product of whose zeroes are $\sqrt{3}$ and $\frac{1}{\sqrt{3}}$.

Given: The sum and product of whose zeroes are $\sqrt{3}$ and $\frac{1}{\sqrt{3}}$ of a quadratic polynomial.

To do: To write the polynomial.

Solution: 

Sum of the quadratic polynomial$=\sqrt{3}$

Product of a quadratic polynomial $=\frac{1}{\sqrt{3}}$

The polynomial is:

$x^{2}-( sum\ of\ the\ polynomial)x+( product\ of\ the\ polynomial)=0$

$\Rightarrow x^{2}-(\sqrt{3})x+( \frac{1}{\sqrt{3}})=0$

$\Rightarrow x^{2}-\sqrt{3}x+\frac{1}{\sqrt{3}}=0$

$\Rightarrow \frac{\sqrt{3}x^{2}-3x+1}{\sqrt{3}}=0$

$\Rightarrow \sqrt{3}x^{2}-3x+1=0$

Thus, the required polynomial is: $\sqrt{3}x^{2}-3x+1=0$.

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Updated on: 10-Oct-2022

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