If (x^2+x-12) divides x^3+ax^2+bx-84 completely,then find the values of a and b.

Asked by ADITHYA V | 2nd Jul, 2013, 09:43: PM

Expert Answer:

x^2+x-12 = (x-3)(x+4)
According to the given condition,
x^2+x-12 = (x-3)(x+4) is a factor of x^3+ax^2+bx-84 = f(x).
 
Hence, f(3) = f(-4) = 0
Therefore, 
27+9a+3b-84=0  or 3a+b-19=0
-64 + 16a-4b-84=0 or 4a-b-37=0
 
Adding these two equations, we get, 7a - 56 = 0 or a = 8
So, b = 19-24 = -5

Answered by  | 2nd Jul, 2013, 11:14: PM

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