Question

24. If both x + 1 and x - 1 are factors of ax^3 + x^2 - 2x + b, find the value of a and b.​

Answer 1

Answer:

Let p(x)=ax3+x2-2x+b

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

Hence, p(-1)=0 and p(1)=0

Hence, p(-1)=a(-1)to the power 3 + (-1)to the power 2 - 2(-1) + b=0

                   = -a+1+2+b=0

                   = a-b=3 _ eq.(1)

Again, p(1)=a(1)to the power 3 + (1)to the power 2 - 2(1) + b=0

                = a+1-2+b=0

                = a+b=1 _ eq.(2)

Solving eq.(1) and (2), we get a=2 b= -1.

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