Question

algebra the alpha β are roots of the quadratic eqn X2-4X-6=0 find alpha sq +beta sq & alpha cube +beta cube .​

Answer 1

Heya!!

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Alfa² + Beta² = ( Alfa + Beta )² - 2 Alfa × Beta

=>

Alfa + Beta = 4 And

Alfa × Beta = -6

=>

Alfa² + Beta² = ( -4 )² - 2( -6 )

=>

Alfa² + Beta² = 16 + 12

=>

Alfa² + Beta² = 28

2)

Alfa³ + Beta³ = ( Alfa + Beta )³ - 3 Alfa × Beta ( Alfa + Beta )

=>

Alfa³ + Beta³ = ( -4 )³ -3 ( -6 ) ( -4 )

=>

Alfa³ + Beta³ = 64 - 72

=>

Alfa³ + Beta³ = -8