Question
11.
Each of the following quadratic equations can be solved by factoring. Which one has only one distinct solution?
(1 point)
Responses
x2 − 5x + 4 = 0
x2 − 5x + 4 = 0
x2 + 4x + 4 = 0
x2 + 4x + 4 = 0
x2 + 5x + 4 = 0
x2 + 5x + 4 = 0
x2 − 4 = 0
x2 − 4 = 0
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Each of the following quadratic equations can be solved by factoring. Which one has only one distinct solution?
(1 point)
Responses
x2 − 5x + 4 = 0
x2 − 5x + 4 = 0
x2 + 4x + 4 = 0
x2 + 4x + 4 = 0
x2 + 5x + 4 = 0
x2 + 5x + 4 = 0
x2 − 4 = 0
x2 − 4 = 0
Skip to navigation
Answers
GPT-4o mini
A quadratic equation has only one distinct solution when it can be expressed as a perfect square trinomial or when the discriminant (b^2 - 4ac) is zero.
Let's analyze the provided options:
1. **x² − 5x + 4 = 0**: This factors to (x - 4)(x - 1) = 0. The solutions are x = 4 and x = 1 (two distinct solutions).
2. **x² + 4x + 4 = 0**: This factors to (x + 2)(x + 2) = 0, which is a perfect square. The solution is x = -2 (one distinct solution).
3. **x² + 5x + 4 = 0**: This factors to (x + 4)(x + 1) = 0. The solutions are x = -4 and x = -1 (two distinct solutions).
4. **x² − 4 = 0**: This factors to (x - 2)(x + 2) = 0. The solutions are x = 2 and x = -2 (two distinct solutions).
The option that has only one distinct solution is:
**x² + 4x + 4 = 0**
Let's analyze the provided options:
1. **x² − 5x + 4 = 0**: This factors to (x - 4)(x - 1) = 0. The solutions are x = 4 and x = 1 (two distinct solutions).
2. **x² + 4x + 4 = 0**: This factors to (x + 2)(x + 2) = 0, which is a perfect square. The solution is x = -2 (one distinct solution).
3. **x² + 5x + 4 = 0**: This factors to (x + 4)(x + 1) = 0. The solutions are x = -4 and x = -1 (two distinct solutions).
4. **x² − 4 = 0**: This factors to (x - 2)(x + 2) = 0. The solutions are x = 2 and x = -2 (two distinct solutions).
The option that has only one distinct solution is:
**x² + 4x + 4 = 0**