Question

If both x+1 and x-1 are factors of ax³+x²-2x+b, find the value of a and b.

Answer 1

Answer:

p(x) = ax^3 + x^2 - 2x + b

g(x) = x + 1 and x - 1

Put x = 1 in p(x):

=> a + 1 - 2 + b = 0

=> a + b = 1

Put x = -1 in p(x):

=> -a + 1 + 2 + b = 0

=> a = 3 + b

Put this in previous eqn:

=> a + b = 1

=> 3 + b + b = 1

=> 2 = -2b

=> b = -1

a = 3 + b = 3 - 1

=> a = 2

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