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Let alpha and beta be the roots of $x^{2} - 4 x + 1 = 0$ . Find the value of alph $a^{3}$ + bet $a^{3}$ .

Class 10Sum and Product of RootsAlgebra — Quadratics

A52
B57
C47
D104

Step-by-Step Solution

Sum = 4, product = 1. alph

a^{3}

+ bet

a^{3} = (s u m)^{3} - 3

(product)(sum) =

64 - 3 (1) (4) = 64 - 12 = 52

.

Answer: A) 52

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