Question

which of the following equations would not have one solution

Answer 1

The answer is d. x² + 6x + 8.

Let's go through all examples.
a. x² + 8x + 16 = 0
    x² + 2 * 4 * x + 4² = 0
    (x + 4)² = 0
    x + 4 = 0
    x = -4         one solution

b. x² + 7x + 49/4 = 0
    x² + 2 * 7/2 * x + (7/2)² = 0
    (x + 7/2)² = 0
    x + 7/2 = 0
    x = -7/2      one solution

c. x² + 10x + 25 = 0
    x² + 2 * 5 * x + 5² = 0
    (x + 5)² = 0
    x + 5 = 0
    x = -5      one solution

This leaves choice d as the equation with more than one solution.