Question

If x3+2x2+ax+b has factor x+1 and x-1 then find a and b
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Answer 1

( x + 1) and ( x - 1) are factors

Hence, 1 and - 1 are the zeros

Put x = 1,

1 + 2 + a + b = 0

a + b = - 3.................(1)

Put x = - 1

-1 + 2 - a + b = 0

-a + b = - 1................(2)

Now add (1) and (2)

a + b - a + b = - 4

2b = - 4

b = - 2

a + b = - 3

a - 2 = - 3

a = - 1