Question

Find the quadratic eq whose roots are 3 and -3

Answer 1

$\huge\red{\underline{\underline{\pink{Ans}\red{wer:}}}}$

$\sf{x^{2}-9=0 \ is \ the \ required \ quadratic \ equation.}$

$\orange{Given:}$

$\sf{The \ roots \ quadratic \ equation \ are}$

$\sf{\implies{3 \ and \ -3}}$

$\sf\pink{To \ find:}$

$\sf{Quadratic \ equation.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Roots \ are \ 3 \ and \ -3}$

$\sf{Let \ \alpha \ be \ 3 \ and \ \beta \ be \ -3}$

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

$\sf{\alpha+\beta=3+(-3)}$

$\sf{\therefore{\alpha+\beta=0...(1)}}$

$\sf{Product \ of \ roots=\alpha×\beta}$

$\sf{\alpha×\beta=3(-3)}$

$\sf{\therefore{\alpha×\beta=-9...(2)}}$

$\sf{Quadratic \ equation \ is}$

$\sf{\implies{x^{2}-(\alpha+\beta)x+(\alpha×\beta)=0}}$

$\sf{from \ (1) \ and (2)}$

$\sf{\implies{x^{2}-0x-9=0}}$

$\sf{\implies{\therefore{x^{2}-9=0}}}$

$\sf\purple{\tt{\therefore{x^{2}-9=0 \ is \ the \ required \ quadratic \ equation.}}}$