Question

Which expression represents the polynomial function m(x) of degree 4 with zeros at 0, 5, and 3-2i?

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

Answer 1

The expression that represents the polynomial function m(x) of degree 4 with zeros at 0, 5, and 3-2i is option a) m(x) = x(x-5)(x-(3-2i))(x-(3+2i)).

Step-by-step explanation:

The expression that represents the polynomial function m(x) of degree 4 with zeros at 0, 5, and 3-2i is option a) m(x) = x(x-5)(x-(3-2i))(x-(3+2i)). To find the expression, we need to use the fact that if a number is a zero of a polynomial function, then (x - zero) is a factor of the polynomial. So, we can write the factors of the polynomial as (x - 0), (x - 5), (x - (3-2i)), and (x - (3+2i)). Multiplying these factors together gives us the expression for the polynomial function.