Find all zeros of the polynomial

Question

Find all zeros of the polynomial g(x) = 6x³ + x² + 294x + 49

Answer 1

Graph g(x). Descartes' rule of signs tells you that there are no positive real roots.

One possibility is -1/6 because 6 divides the coefficient of the cubic term...and in fact this is a root.

Then divide g(x) by 6x + 1 to get quotient x² + 49 for which the roots are 7i and -7i.