Question

If alpha beta are roots px2+qx+r=0 then find alpha cube+beta cube & alpha square beta+alpha beta square

Answer 1

Answer:

α³ + β³ = (3pqr -q³)/p³

α²β + αβ² = -qr/p²

Step-by-step explanation:

alpha beta are roots px2+qx+r=0

α + β = -q/p   ( sum of roots)

αβ = r/p        ( products of Roots)

α³ + β³ = (α + β)³ -3αβ(α + β)

=> α³ + β³ = (-q/p)³ -3(r/p)(-q/p)

=> α³ + β³ = -(q/p)³ + 3qr/p²

=> α³ + β³ = (1/p³)(-q³ + 3pqr)

=> α³ + β³ = (3pqr -q³)/p³

α²β + αβ² = αβ(β + α)

=> α²β + αβ² = (r/p)(-q/p)

=> α²β + αβ² = -qr/p²