Grade 12Algebra
If p and q are the roots of the equation: ax^2 + bx + c then find p^5 + q^5 in terms of a, b and c.
If p and q are the roots of the equation: ax^2 + bx + c then find p^5 + q^5 in terms of a, b and c.
1 Answer
Mohamed Harithkhan
ax^2 + bx + c = 0
p+q = -b/a
pq = c/a
(p+q)^5 = (p+q)^2 * (p+q)^2 * (p+q)
= p5 + 5p4q + 10p3q2 + 10p2q3 + 5pq4 + q5
p5 + q5 = (p + q)5 - 5p4q - 10p3q2 - 10p2q3 - 5pq4
= (p + q)5 - 5pq* p3- 10(pq)2*p - 10(pq)2*q - 5(pq)q3
= (p + q)5 - 5pq( p3 + q3) - 10(pq)2(p + q)
= (p + q)5 - 5pq{(p + q)3 - 3pq2 – 3p2q} - 10(pq)2(p + q)
= (p + q)5 - 5pq{(p + q)3 - 3pq(p+q)} - 10(pq)2(p + q)
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