Question

If the polynomial x^3 +2x^2 +ax+b has factors x+1 and x-1, find the values of a and b

Answer 1

Answer:

a = -1 and b = -2

Step-by-step explanation:

Let p(x) = $x^3+2x^2+ax+b$

(x+1) and (x-1) are the factors of p(x).

∴ (-1) and 1 are the zeroes of p(x)

p(-1) = $(-1)^3+2(-1)^2+a(-1)+b$

      =(-1)+2-a+b=0

      =1-a+b=0

      = -a+b=-1--------->(i)

p(1) = $(1)^3+2(1)^2+a(1)+b$

     = 1+2+a+b=0

     = 3+a+b=0

     = a+b=-3 --------->(ii)

Solving equation (i) and (ii), we get,

b= -2 and a= -1.

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