If alpha and beta are the roots of quadratic equation x ^ - 4x-6=0 find the value of 1} alpha square + betasquare 2} alpha cube+ beta cube
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Answer: 4 and -8
Step-by-step explanation:
α+β=4 and αβ=6
1)
α²+β²=(α+β)²-2αβ
=4²-2×6
=16-12=4
2)
(α+β)³=α³+3α²β+3αβ²+β³=α³+β³+3αβ(α+β)
∴α³+β³=(α+β)³-3αβ(α+β)
=4³-3×6×4
=64 - 72
= -8
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