Question

Three roots of a polynomial equation with real coefficients are 3, 5 – 3i, and −3i. Which of the following numbers must also be a root of the equation?

a. 5 + 3i only
b. −3 and 5 + 3i only
c. 5 + 3i and 3i only
d. −3, 5 + 3i, and 3i

Answer 1

9514 1404 393

Answer:

c. 5 + 3i and 3i only

Explanation:

The conjugates of the given complex roots must also be roots of the equation.

The conjugate of 5 -3i is 5 +3i.

The conjugate of -3i is 3i.

So, 5+3i and 3i must also be roots of the equation.