Find a cubic polynomial with real coefficients having roots x = -2 and x = 1 + 4i. Assume a lead coefficient of 1. A) P(x) = x³ + 13x + 34 B) P(x) = x³ + 13x - 34 C) P(x) = x³ + 4x² + 21x + 34 D) P(x) = x³ - 4x² + 21x - 34

Question

Quizplus · Accepted Answer

Since -2 is a root, (x + 2) is a factor. Since 1 + 4i is a root, so is its conjugate 1 - 4i. Therefore, (x - 1 + 4i)(x - 1 - 4i) = x^2 - 2x + 17 is also a factor. Thus, P(x) = (x + 2)(x^2 - 2x + 17) = x^3 + 13x + 34.

Find a Cubic Polynomial with Real Coefficients Having Roots X