Problem: The equation has
Answer Choices:
A. no real roots
B. exactly two distinct negative roots
C. exactly one negative root
D. no negative roots, but at least one positive root
E. none of these
Solution:
If is a root, then ; if were negative, the left side of this equation would be positive and the right side would be negative. Also, the polynomial has a positive value at and a negative value at . (The fact that the polynomial has no negative roots also follows directly from Descartes' rule of signs.)