Question

I really need help with this. Can anyone help me please?

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.
3,-2+2i

Thank you!

Answer 1

• f(x) = x³ + x² - 4x - 24

Explanation:

Since one of zero's is complex number, its conjugate should also be a zero of the given polynomial.

• The conjugate of -2 + 2i is -2 - 2i

The polynomial is going to be:

• f(x) = (x - a)(x - b)(x - c) with minimum of degree 3, with zero's a, b and c.

Substitute zero's:

• f(x) = (x - 3)(x - (-2 + 2i))(x - (-2 - 2i)) =
• (x - 3)(x² - x (-2 + 2i -2 - 2i) + (-2 + 2i)(-2 - 2i)) =
• (x - 3)(x² + 4x + 8) =
• x³ + x² - 4x - 24