In Problem, use Problem and (3) to factor the given quadratic polynomial if the indicated...

In Problem, use Problem and (3) to factor the given quadratic polynomial if the indicated complex number is one root.

Problem

If z1 is a root of a polynomial equation with real coefficients, then its conjugate  is also a root. Prove this result in the case of a quadratic equation az2 + bz + c = 0, where a ≠ 0, b, and c are real. Start with the properties of conjugates given in (1) and (2).

 (1)

 (2)

(3)