Question

If alpha and beta are the roots of the equation 3x^2+2x+1=0 whose roots are 1/ alpha and 1/ beta

Answer 1

$\huge\bigstar\sf\red{Answer:}$

$\sf{3x^{2}+2x+1=0}$

$\sf{\therefore{\alpha+\beta=\dfrac{-2}{3}...(1)}}$

$\sf{\therefore{\alpha\beta=\dfrac{1}{3}...(2)}}$

$\sf{\therefore{\alpha^{2}+\beta^{2}=(\frac{-2}{3})^{2}-2(\frac{1}{3})}}$

$\sf{=\frac{4-6}{9}}$

$\sf{=\frac{-2}{9}...(3)}$

$\sf{For \ new \ quadratic \ equation}$

$\sf{Sum \ of \ roots=\frac{1}{\alpha}+\frac{1}{\beta}}$

$\sf{=\frac{\alpha^{2}+\beta^{2}}{\alpha\beta}=\frac{-2}{3}}$

$\sf{Product \ of \ roots=\frac{1}{\alpha}\times\frac{1}{\beta}=3}$

$\sf{x^{2}-\frac{2x}{3}+3}$

$\sf{\longmapsto{3x^{2}-2x+9, \ is \ required \ equation.}}$