Question

and beta are the zeros of polynomial 2 X square + 3 x minus 6 find the value of Alpha square beta + alpha beta square ​

Answer 1

Question : Alpha and beta are the zeros of polynomial 2 X square + 3 x minus 6 find the value of Alpha square beta + alpha beta square ​

Answer:

Quadratic equation is 2x²+3x-6.

Compare this with ax²+bx+c and sub. values in below equations.

$\implies \alpha +\beta =\frac{-b}{a}\\\\ \implies \alpha .\beta =\frac{c}{a}$

Here , a = 2 , b = 3 , c = -6

$\implies \alpha +\beta =\frac{-3}{2}\\\\ \implies \alpha .\beta =\frac{-6}{2}=-3$

Now , Required

$\alpha ^2 \beta +\alpha \beta ^2\\\\\implies \alpha .\beta (\alpha +\beta )\\\\\implies -3(\frac{-3}{2} )\\\\\implies \frac{9}{2}$