15. One of the roots of the equation x^{3} – 7x^{2} + 25x – 39 = 0 is 3. What are the other 2 roots of this equation?
A. –1 and 5 |
B. –1 and 13 |
C. 2–(17)^{1/2} and 2+(17)^{1/2} |
D. 2 – 3i and 2 + 3i |
E. 3 – 2i and 3 + 2i |
Solution: The answer is D
Since 3 is a root, then (x-3) is a factor of x^{3} – 7x^{2} + 25x – 39. Use the method of long division to find another factor, as follows:
Since x^{2} – 4x + 13 is not factorable, use the quadratic formula to find the other two roots.