F. 4 Maths
2013-12-30 10:38 pm
Given that α and β are the roots of the quadratic equationx2+ 3x –5= 0(a)Express α2in the form a + bα(b)Hence find thevalue ofα3 + 14β
回答 (1)
2013-12-31 12:30 am
✔ 最佳答案
(a) Since x^2 + 3x - 5 = 0 and a is a root of the equation,so a^2 + 3a - 5 = 0
a^2 = 5 - 3a.
(b)
Since a^2 + 3a - 5 = 0
a^3 + 3a^2 - 5a = 0
a^3 = 5a - 3a^2 = 5a - 3(5 - 3a) = 5a - 15 + 9a = 14a - 15
So a^3 + 14b = 14a - 15 + 14b = 14(a + b) - 15 = 14(-3) - 15 = - 42 - 15 = - 57.
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