Question

if alpha and beta are the zeros of polynomial x squared minus xminus 6 find a polynomial whose zeros are Alpha square by Beta square and beta square by Alpha square

Answer 1

x²- x - 6 = 0
α+ β = 1
αβ = -6
now,
α²/β² + β²/α²
=(α4+β4)/(αβ)²
={(α²)²+(β²)²}/(αβ)