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

Question

Responses

x^2−5x+4=0
x squared minus 5 x plus 4 equals 0

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

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

x^2−4=0

Answer 1

A quadratic equation has only one distinct solution when its discriminant (b² - 4ac) is equal to zero.

Let's analyze the provided equations:

1. x² − 5x + 4 = 0

   • a = 1, b = -5, c = 4
   • Discriminant: (-5)² - 4(1)(4) = 25 - 16 = 9 (two distinct solutions)

2. x² + 5x + 4 = 0

   • a = 1, b = 5, c = 4
   • Discriminant: (5)² - 4(1)(4) = 25 - 16 = 9 (two distinct solutions)

3. x² + 4x + 4 = 0

   • a = 1, b = 4, c = 4
   • Discriminant: (4)² - 4(1)(4) = 16 - 16 = 0 (one distinct solution)

4. x² − 4 = 0

   • a = 1, b = 0, c = -4
   • Discriminant: (0)² - 4(1)(-4) = 0 + 16 = 16 (two distinct solutions)

The equation that has only one distinct solution is:

x² + 4x + 4 = 0.