Question

For which values of a and b, the zeroes of q(x) = x3 + 2x2 + a are also the zeroes of the polynomial p(x) = x5 - x4 - 4x3 + 3x2 + 3x + b ? Which zeroes of p(x) are not the zeroes of p(x) ? ​

Answer 1

If (x3 + 2x2 + a) is a factor of (x5 – x4 – 4x3 + 3x2 + 3x + b), then remainder should be zero. For a = -1 and b = – 2, the zeroes ofq(x) are also the zeroes of the polynomial p(x). Hence, the zeroes of p(x) are land 2 which are not the zeroes of q(x).

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