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

Question

Responses

x2−4=0
x squared minus 4 equals 0

x2−5x+4=0
x squared minus 5 x plus 4 equals 0

x2+5x+4=0
x squared plus 5 x plus 4 equals 0

x2+4x+4=0

Answer 1

To determine which equation has only one distinct solution, we can look for a quadratic equation that can be factored into a perfect square.

1. \( x^2 - 4 = 0 \)
   Factors to \( (x-2)(x+2) = 0 \)
   Solutions: \( x = 2 \) and \( x = -2 \) (two distinct solutions)

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

3. \( x^2 + 5x + 4 = 0 \)
   Factors to \( (x+4)(x+1) = 0 \)
   Solutions: \( x = -4 \) and \( x = -1 \) (two distinct solutions)

4. \( x^2 + 4x + 4 = 0 \)
   Factors to \( (x+2)(x+2) = 0 \)
   Solution: \( x = -2 \) (one distinct solution, repeated)

Thus, the equation that has only one distinct solution is:

\( x^2 + 4x + 4 = 0 \).