Question

of p²-2p-7=0
If α and β are the roots
then find α^2β +αβ^2​

Answer 1

Answer:

GIVEN QUADRATIC EQUATION :-

=》 p² - 2p - 7 = 0

$its \: \: root \: \: is \: \: \alpha \: \: \: and \: \: \: \beta$

TO FIND :-

${ \alpha }^{2} \beta + \alpha { \beta }^{2}$

WE SHOULD WRITE THIS AS :-

$\alpha \beta ( \alpha + \beta )$

WE KNOW THAT :-

$sum \: \: of \: \: roots \: = \alpha + \beta \\ \\ multiply \: \: of \: \: roots \: = \alpha . \beta$

SUM OF ROOTS = 2

MULTIPLE OF ROOTS = -7

SO -

$\alpha \beta ( \alpha + \beta ) = 2( - 7) = - 14$

HOPE IT'S HELP YOU...