Inactive Tutor answered • 12/30/14
Tutor
New to Wyzant
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) ( x2 - 4 x +5) = x3 - 11x +20 = P(X)
Inactive 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
x3 - 11 x +20 is the lowest degree (three) polynomial with real coefficients having the zeros -4 and 2 + i.
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12/30/14
Inactive Tutor
12/30/14