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Answers
Given f(x) = x^3 + 2x^2 - 5ax - 7.
Given that f(x) by divisible by (x + 1).
By remainder theorem, we get
= > x + 1 = 0
= > x = -1.
f(-1) = (-1)^3 + 2(-1)^2 - 5a(-1) - 7
= -1 + 2 + 5a - 7
= 5a - 6
= r
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Given g(x) = x^3 + ax^2 - 12ax + 6
Given that g(x) is divisible by x - 2.
By remainder theorem, we get
= > x - 2 = 0
= > x = 2.
f(2) = (2)^3 + a(2)^2 - 12a(2) + 6
= 8 + 4a - 24a + 6
= 14 - 20a.
= s.
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Given 2r + s = 6
= > 2(5a - 6) + (14 - 20a) = 6
= > 10a - 12 + 14 - 20a = 6
= > -10a + 2 = 6
= > -10a = 4
= > a = -4/10
= > a = -2/5.
Hope this helps!