Question

If both (x+1) and(x-1) are factors of ax³+x²-2x+b.
Find the values of a and b.​

Answer 1

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Let f(x) = ax3 + x2 − 2x + b be the given polynomial.

By factor theorem, if (x+1) and (x-1) both are factors of the polynomial f (x).

if f(−1) and f(1) both are equal to zero.

Hence, the value of a and b are 2 and −1 respectively.