If #(x^2-5x-6)/(x^3+ax^2+bx+c# simplifies to #1/(x+2)#, then a + b + c = ?

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Answer 1 · 2017-11-09T05:59:31

# -21.#

Given that, #(x^2-5x-6)/(x^3+ax^2+bx+c)=1/(x+2).#

By Cross Multiplication, we get,

#x^3+ax^2+bx+c=(x^2-5x-6)(x+2), i.e., #

#=(x-6)(x+1)(x+2),#

#=x(x^2-5x-6)+2(x^2-5x-6),#

#=(x^3-5x^2-6x)+(2x^2-10x-12).#

#rArr x^3+ax^2+bx+c=x^3-3x^2-16x-12.#

Comparing the co-efficients of polynomials on both sides, we have

#a=-3, b=-16, and, c=-12.#

#:. a+b+c=-21,# as desired.

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