Question

Let us form the equation whose roots are reciprocals to the roots of the equation x²+px+1=0.​

Answer 1

Answer:

Given equation is :  $x^2+px+1=0$

Let us consider the roots as α and β

=> Sum of the roots (α+β) = $\frac{-b}{a}$ = $\frac{-p}{1}$

=> Product of the roots (αβ) = $\frac{c}{a} = \frac{1}{1}$

Reciprocal of roots = $\frac{1}{\alpha } ,\frac{1}{\beta }$

Equation with reciprocal roots is

=> $x^2-(\frac{1}{\alpha } +\frac{1}{\beta } )x+(\frac{1}{\alpha \beta})=0$

=> $x^{2} -(\frac{\alpha \beta }{\alpha +\beta } )x+\frac{1}{\alpha \beta } =0$

=> $x^{2} -(\frac{1}{-p})x+1=0$

=> $px^{2} +x+1=0$

Answer 2

Answer:

go through the pic carefully