if you have a cubic polynomial with one real root and one imaginary root, why does the third root have to be imaginary

Question

Classifying Polynomials: All polynomials are classified by degree and number of terms

Answer 1

If one of the roots of a cubic is a complex root, then so also is one other root.

That's because complex roots always come in pairs, as complex conjugates.

If one root is r1 = a + b.i, then the other (complex) root is r2 = a - b.i

a + b.i and a - b.i are called complex conjugates.

So, if you have been given one complex root, then simply take its complex conjugate as the other complex root.