Question

Question
How many solutions are in the solution set for each quadratic equation below?(3 points)
5x2=50
This quadratic equation would have
solution(s).

3x2=−12
This quadratic equation would have
solution(s).

8x2=0
This quadratic equation would have
solution(s).

Answer 1

To determine the number of solutions for each quadratic equation, we can rewrite them in the standard form \(ax^2 + bx + c = 0\) and consider their discriminants.

1. **For the equation \(5x^2 = 50\)**:
- Rearranging gives: \(5x^2 - 50 = 0\)
- Dividing by 5: \(x^2 - 10 = 0\)
- This can be written as \(x^2 = 10\).
- The solutions are \(x = \pm \sqrt{10}\), which means there are **2 solutions**.

2. **For the equation \(3x^2 = -12\)**:
- Rearranging gives: \(3x^2 + 12 = 0\)
- Dividing by 3: \(x^2 + 4 = 0\)
- We write \(x^2 = -4\).
- Since the square of a real number cannot be negative, there are **0 solutions** in the real number system (the solutions are complex).

3. **For the equation \(8x^2 = 0\)**:
- Rearranging gives: \(8x^2 = 0\)
- Dividing by 8: \(x^2 = 0\).
- The only solution is \(x = 0\), which means there is **1 solution**.

### Summary:
- **5x² = 50**: 2 solutions
- **3x² = -12**: 0 solutions
- **8x² = 0**: 1 solution