EQUAÇÕES POLINOMIAIS - PUCSP

Solution to the question whose statement is: "(PUCSP) The polynomial p(x) = x³ + 4x² + 5x + k admits three real roots such that one of them is the sum of the other two. Under these conditions, if k is the real part of the complex number z = k + 2i, then z (A) is a pure imaginary number. (B) has a modulus equal to 2. (C) is the conjugate of −2 − 2i. (D) is such that z² = 4i. (E) has a principal argument equal to 45⁰."