Question

Each of the following quadratic equations can be solved by factoring. Which equation has only one distinct solution?(1 point)
Responses

A) x^2+5x+4=0
x squared plus 5 x plus 4 equals 0

B) x^2+4x+4=0
x squared plus 4 x plus 4 equals 0

C) x^2−4=0
x squared minus 4 equals 0

D) x^2−5x+4=0

Answer 1

To determine which quadratic equation has only one distinct solution, we can look for a perfect square trinomial or check if the discriminant (b² - 4ac) is zero.

We can analyze each equation:

A) \(x^2 + 5x + 4 = 0\)
This factors to \((x + 1)(x + 4) = 0\)
Solutions: \(x = -1\) and \(x = -4\) (two distinct solutions)

B) \(x^2 + 4x + 4 = 0\)
This factors to \((x + 2)(x + 2) = 0\)
Solution: \(x = -2\) (one distinct solution)

C) \(x^2 - 4 = 0\)
This factors to \((x - 2)(x + 2) = 0\)
Solutions: \(x = 2\) and \(x = -2\) (two distinct solutions)

D) \(x^2 - 5x + 4 = 0\)
This factors to \((x - 1)(x - 4) = 0\)
Solutions: \(x = 1\) and \(x = 4\) (two distinct solutions)

From this analysis, the equation that has only **one distinct solution** is:
**B) \(x^2 + 4x + 4 = 0\)**.