question_answer

Case Study : Q. 26 to 30

Ramesh was asked by one of his friends to find the polynomial whose zeroes are \[\frac{-2}{\sqrt{3}}\] and \[\frac{\sqrt{3}}{4}\]. He obtained the polynomial as shown below:

Let \[\alpha =\frac{-2}{\sqrt{3}}\] and \[\alpha =\frac{\sqrt{3}}{4}\]

\[\Rightarrow \,\,\,\,\,\,\,\alpha +\beta =\frac{-2}{\sqrt{3}}+\frac{\sqrt{3}}{4}=\frac{-8+1}{4\sqrt{3}}=\frac{-7}{4\sqrt{3}}\]

\[\Rightarrow \,\,\,\,\,\,\,\alpha \beta =\frac{-2}{\sqrt{3}}\times \frac{\sqrt{3}}{4}=\frac{-1}{2}\]

Required polynomial \[={{x}^{2}}-(\alpha +\beta )x+\alpha \beta \]

\[={{x}^{2}}-\left( \frac{-7}{4\sqrt{3}} \right)x+\left( \frac{-1}{2} \right)\]

\[={{x}^{2}}+\frac{7x}{4\sqrt{3}}-\frac{1}{2}\]

\[=4\sqrt{3}{{x}^{2}}+7x-2\sqrt{3}\]

His another friend Kavita pointed out that the polynomial obtained is not correct.

Based on the above situation, answer the following questions:

Is the claim of Kavita correct?

A) Yes

B) No

C) Can't say

D) None of these