question_answer

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

Answer:

Given, sum of zeroes, \[(S)=\sqrt{3}\]

Product of zeroes, \[(P)=\frac{1}{\sqrt{3}}\]

Quadratic polynomial is given as, \[{{x}^{2}}-Sx+P\]

\[={{x}^{2}}-\sqrt{3}x+\frac{1}{\sqrt{3}}\]

\[=\frac{\sqrt{3}{{x}^{2}}-3x+1}{\sqrt{3}}\]

\[=\frac{1}{\sqrt{3}}(\sqrt{3}{{x}^{2}}-3x+1)\]