Question

If ax²+bx+c has roots alpha and beta find

alpha/(beta)²+(beta)²/alpha

Answer 1

Answer:

Since α , β are the roots of the equation x²+ax+b = 0

So

α + β = - a

α β = b

Now

α³ + β³

= ( α + β) ³ - 3 αβ ( α + β)

= ( - a³ +3ab)

Therefore

( α² / β ) + ( β ² /α)

= ( α³ + β ³ ) / α β

= ( - a³ +3ab) / b

Answer 2

see the attachment above!!♡♡