If ax²+bx+c has roots alpha and beta find
alpha/(beta)²+(beta)²/alpha
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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