Question

Find the cubic equation with integral coefficients sum of whose roots are 3 and 2i.

A) x^3 − 3x^2 + 13x - 14 = 0
B) x^3 − 3x^2 − 13x - 14 = 0
C) x^3 − 3x^2 + 13x + 14 = 0
D) x^3 − 3x^2 − 13x + 14 = 0

Answer 1

The cubic equation with integer coefficients sum of whose roots are 3 and 2i is x^3 - 3x^2 + 4x + 12 = 0.

Step-by-step explanation:

To find the cubic equation with integral coefficients whose sum of roots are 3 and 2i, we can use the fact that complex roots come in conjugate pairs. So, if 2i is a root, then -2i is a root as well. The sum of the roots is 3, so the other root must be 3 - 2i. Using Vieta's formulas, the cubic equation will be:

x^3 - 3x^2 + 4x + 12 = 0