Question #10643

Find the value of a and b so that (x+1) and (x-1)are the factors ofx4+ax3-3x2+2x+b.

Expert's answer

if x+1 and x-1 are factors of f(x) then f(1)=f(-1)=0

So after

substitution -1 and 1 we'll

get:

1-a-3-2+b=0

1+a-3+2+b=0

Then

b-a=4

b+a=0

Finally,

b=2, a=-2

So after

substitution -1 and 1 we'll

get:

1-a-3-2+b=0

1+a-3+2+b=0

Then

b-a=4

b+a=0

Finally,

b=2, a=-2

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