Question

if alpha beta are the roots of equation X square + 2 x minus 1 is equals to zero then the equation whose roots are Alpha square and beta square is ​

Answer 1

$\textbf{Given:}$

$\text{ \alpha and \beta are roots of x^2+2x-1=0 }$

$\textbf{To find:}$

$\text{The quadratic equation having roots \alpha^2 and \beta^2 }$

$\text{Sum of the roots= \frac{-b}{a} }$

$\implies\,\alpha+\beta=\frac{-2}{1}$

$\implies\,\bf\alpha+\beta=-2$

$\text{Product of the roots= \frac{c}{a} }$

$\implies\,\alpha\beta=\frac{-1}{1}$

$\implies\,\bf\alpha\beta=-1$

$\text{Now}$

$\alpha^2+\beta^2=(\alpha+\beta)^2-2\,\alpha\beta$

$\alpha^2+\beta^2=(-2)^2-2(-1)$

$\alpha^2+\beta^2=4+2$

$\implies\bf\alpha^2+\beta^2=6$

$\alpha^2\beta^2=(\alpha\beta)^2$

$\alpha^2\beta^2=(-1)^2$

$\implies\bf\alpha^2\beta^2=1$

$\text{The required quadratic equation is}$

$x^2-(\alpha^2+\beta^2)x+\alpha^2\beta^2=0$

$\implies\bf\,x^2-6x+1=0$

Find more:

If alpha,beta are the roots of equation x^2-5x+6=0 and alpha > beta then the equation with the roots (alpha+beta)and (alpha-beta) is

https://brainly.in/question/5731128

Answer 2

Answer:

hsjsknssjkddnjdszmgjektudhtd!udtmutd!utdh!gd thd!htdfhx!hfxh

ykyf

Step-by-step explanation:

ggujcndksmshidjdd