If the polynomial is to have real coefficients (the usual criterion) , then 2 - i must also be a zero.

(x - (-4) ) (x - (2 + i)) ( x - (2 -i) ) = P(x)

FOIL the last two terms to get

(x + 4) ( x

^{2}- 4 x +5) = x^{3}- 11x +20 = P(X)Richard P.

tutor

The problem statement did not restrict the degree of the polynomial, nor insist that the coefficients be real. However, there is almost always an implicit requirement that the coefficients be real. The polynomial

x

^{3}- 11 x +20 is the lowest degree (three) polynomial with real coefficients having the zeros -4 and 2 + i.
Report

12/30/14

Mitiku D.

12/30/14