Problema Solution
Find a fourth-degree polynomial with integer coefficients that has zeros 2i and −1, with −1 a zero of multiplicity 2. (Use x for the variable.)
Answer provided by our tutors
the 4-degree polynomial with integer coefficients that has zeros 2i and −1, with −1 a zero of multiplicity 2
the zeros are 2i, -2i, -1, and -1
p(x) = a (x - 2i)(x + 2i)(x - (-1))(x - (-1))
p(x) = a (x^2 + 4)(x^2 - 2x + 1)
p(x) = a ( x^4 - 2x^3 + 5x^2 - 8x + 4)
one such polynomial is for a = 1
p(x) = x^4 - 2x^3 + 5x^2 - 8x + 4