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If alpha and beta are the roots of the equation x^2-x-3,find 4 alpha square + beta cube

If alpha and beta are the roots of the equation x^2-x-3,find 4 alpha square + beta cube

Grade:10

1 Answers

sonika p
129 Points
4 years ago
since, alpha, beta are roots 
let alpha =a, beta =b
thus, a^2 – a – 3 =0
a^2 = a+3
a+b =1, ab = -3
a^2 = 1 – b +3 = 4- b.....(1)
similarly, b^2 = 4 – a.....(2)
4a^2 + b^3 = 4(4-b) + (4-a)b = 16 – 4b + 4b – ab = 16 +3 = 19
Therefore, 4alpha square + beta cube = 19
 

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