Question

2. Here is a graph of the equation y = x² + 4x + 5.

Which statement is true about the solutions to the
equation x² + 4x + 5 = 0?
A. The equation has no solution.
B. The equation has one solution: 5.
C. The equation has two solutions: -2 and 0.
D. The equation has infinitely many solutions.
2

Answer 1

The correct statement about the solutions of the equation x² + 4x + 5 = 0 is that it has no real solutions, as the discriminant is negative. Therefore, option A is the correct answer.

Step-by-step explanation:

The statement that is true about the solutions to the equation x² + 4x + 5 = 0 can be determined using the quadratic formula, which is applicable for equations of the form ax² + bx + c = 0.

To determine whether the equation has real solutions, we can calculate the discriminant (b² - 4ac).

In this case, a = 1, b = 4, and c = 5.

The discriminant is thus (4²) - (4*1*5) = 16 - 20, which equals -4.

A negative discriminant indicates that the equation has no real solutions.

Therefore, the correct statement about this equation is that it has no real solution, which corresponds to option A.