Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the zeros 4 and 3−i.

Question

Please help me. Also please explain.

Answer 1

The least degree will be 3, remembering that complex roots come in conjugate pairs. So, given that (3 - i) is a root, then (3 + i) is another root. The real root, 4, is easy, giving the linear factor (x - 4).

f(x) = (x - 4) (x - (3 + i))(x - (3 - i)) factored form or ...

f(x) = (x - 4) (x² - 6x + 10) = x³ - 10x² - 14x - 40. in standard form