Question

What is the standard form of the polynomial function of least degree with real coefficients and a leading coefficient of one, and zeros at 0, 4, and (3 + 2i)?

Answer 1

The standard form of the polynomial function with zeros at 0, 4, and (3 + 2i) is f(x) = x(x - 4)(x - (3 + 2i))(x - (3 - 2i)).

Step-by-step explanation:

The standard form of a polynomial function with zeros at 0, 4, and (3 + 2i) is found by using the zero product property. Since 0 is a zero, the polynomial function has a factor of x. Since 4 is a zero, the polynomial function has a factor of (x - 4). Finally, since (3 + 2i) is a zero, its complex conjugate, (3 - 2i), must also be a zero. So the polynomial function has a factor of (x - (3 + 2i))(x - (3 - 2i)). Multiplying these factors together gives:

f(x) = x(x - 4)(x - (3 + 2i))(x - (3 - 2i))