Question

If $\alpha and\beta$ are the roots of $x^2+p=0$ where p is a prime then which equation has the roots $\frac{1}{\alpha }\&\frac{1}{\beta }$?

• A. $\frac{1}{x^2}+\frac{1}{p}=0$
• B. $p{x}^2+1=0$
• C. $p{x}^2-1=0$
• D. $\frac{1}{x}+\frac{1}{p^2}=0$

Answer 1

The correct option is B $p{x}^2+1=0$

Given equation $x^2+p=0$

Then sum of roots=$\alpha +\beta$ =$\frac{-0}{1}=0$

And multiple of roots=$\alpha \beta$=$\frac{p}{1}=0$

Then the roots are $\frac{1}{\alpha }\to \frac{1}{\beta }$

Then sum of roots are=$\frac{1}{\alpha }+\frac{1}{\beta }$=$\frac{1}{0}$=0

Or multiple of roots=$\frac{1}{p}$

Then new equation= $x^2+\frac{1}{p}=0\Rightarrow p{x}^2+1=0$