GATE | GATE 2017 MOCK II | Question 36

If P, Q are the roots of the quadratic equation x2 + ax + b. Find the value of P3 +Q3.

(A) 3ab – a3
(B) 3ab – b3
(C) 3(a2)(b2) – a3
(D) 3(a2)(b2) – b3

Answer: (A)

Explanation: For any quadratic equation which is off the form x2+ax+b=0

1. Sum of the roots P+Q = -a
2. Product of the roots PQ = b
=> P3 + Q3 = (P+Q)(P2+Q2-PQ)
=> (P+Q)((P+Q)2-2PQ-PQ)
=> (P+Q)((P+Q)2-3PQ)
=> (-a)(a2-3b)
=> 3ab – a3

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