Question

Which polynomial has roots of 1-2i and 5?

Answer 1

If roots of 1-2i and 5 are roots of the polynomial, then factors are [ x - (1 - 2i)], [x - 5], and [x + (1 + 2i)].

Recall the theorem that non-Real roots appear in conjugate pairs.

Your polynomial is the product of these factors: [ x - (1 - 2i)], [x - 5], and [x + (1 + 2i)].