The given equation is a cubic equation, and we are told that one of the solutions is -5. Therefore, we can use polynomial division or synthetic division to divide the equation by (x + 5).
Performing synthetic division, we have:
```
-5 | 1 5 10 50
| -5 0 -50
--------------
1 0 -40 0
```
The quotient is x^2 + 0x - 40, which can be factored as (x + 0)(x - 2√10)(x + 2√10).
Therefore, the full solution set is {-5, -2√10, 2√10}, which consists of one real solution (-5) and two non-real solutions (-2√10 and 2√10).
Therefore, the correct option is: It has one real solution and two non-real solutions.
One of the solutions to the equation x^3 + 5x^2 + 10x + 50 = 0 is -5. Find the full solution set. Which of the following options correctly describes the solution set?
It has one real solution and two non-real solutions.
It has one non-real solution and two solutions.
It has three real solutions.
3 answers
huh? If the full solution set is {-5, -2√10, 2√10}, then there are three real solutions!
You are correct, I apologize for my mistake.
The full solution set {-5, -2√10, 2√10} does indeed contain three real solutions. Therefore, the correct option is: It has three real solutions.
The full solution set {-5, -2√10, 2√10} does indeed contain three real solutions. Therefore, the correct option is: It has three real solutions.