Question

Given m(x) is a polynomial function of degree 4 with zeros at 0, 5, and 3 - 2i, write a possible expression for m(x).

a. m(x) = x(x - 5)(x - 3 + 2i)(x - 3 - 2i)
b. m(x) = (x - 5)(x - 3 + 2i)(x - 3 - 2i)
c. m(x) = x(x - 5)(x + 3 + 2i)(x + 3 - 2i)
d. m(x) = (x - 5)(x + 3 + 2i)(x + 3 - 2i)

Answer 1

The polynomial function with zeros at 0, 5, and 3 - 2i can be expressed as m(x) = x(x - 5)(x - 3 + 2i)(x - 3 - 2i).

Step-by-step explanation:

The polynomial function with zeros at 0, 5, and 3 - 2i can be expressed as:

m(x) = x(x - 5)(x - 3 + 2i)(x - 3 - 2i)

In this expression, x represents the independent variable, and the factors (x - 5), (x - 3 + 2i), and (x - 3 - 2i) represent the zeros of the polynomial. The complex conjugate zeros (3 + 2i) and (3 - 2i) ensure that the polynomial has real coefficients.