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# CBSE Class 10 Answered

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 | 02 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 | 02 Jul, 2013, 11:14: PM

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