Question

If the polynomial x²+ax+b has alpha and beta has roots find
alpha/(beta)² + (beta)²/alpha

Answer 1

Answer:

Step-by-step explanation:

alpha/(beta)² + (beta)²/alpha

α2++2αβ+β2=(α+β)2=b2a2

so our final outcome will be

α3+β3=(α+β)(α2−αβ+β2)=−ba(α2+2αβ+β2−3αβ)=−ba(b2a2−3ca)=−b3−3abca3

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Answer 2

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