which equation has only one distinct solution

a. x^2 + 4x + 4 = 0
b. x^2 + 5x + 4 = 0
c. x^2 - 4 = 0
d. x^2 - 5x + 4 = 0

1 answer

To determine which equation has only one distinct solution, we need to look for an equation where the discriminant is zero. The discriminant \( D \) for a quadratic equation of the form \( ax^2 + bx + c = 0 \) is given by the formula:

\[ D = b^2 - 4ac \]

If the discriminant \( D = 0 \), the equation has one distinct solution (also called a repeated or double root).

Let's calculate the discriminant for each option:

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

  • Here, \( a = 1 \), \( b = 4 \), \( c = 4 \)
  • Discriminant: \( D = 4^2 - 4 \times 1 \times 4 = 16 - 16 = 0 \)

b. \( x^2 + 5x + 4 = 0 \)

  • Here, \( a = 1 \), \( b = 5 \), \( c = 4 \)
  • Discriminant: \( D = 5^2 - 4 \times 1 \times 4 = 25 - 16 = 9 \)

c. \( x^2 - 4 = 0 \)

  • Here, \( a = 1 \), \( b = 0 \), \( c = -4 \)
  • Discriminant: \( D = 0^2 - 4 \times 1 \times (-4) = 0 + 16 = 16 \)

d. \( x^2 - 5x + 4 = 0 \)

  • Here, \( a = 1 \), \( b = -5 \), \( c = 4 \)
  • Discriminant: \( D = (-5)^2 - 4 \times 1 \times 4 = 25 - 16 = 9 \)

Now, summarizing the results:

  • a: \( D = 0 \) (one distinct solution)
  • b: \( D = 9 \) (two distinct solutions)
  • c: \( D = 16 \) (two distinct solutions)
  • d: \( D = 9 \) (two distinct solutions)

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

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

Similar Questions
  1. which equation has only one distinct solution?a x^2 + 4x + 4 = 0 b x^2 + 5x + 4 = 0 c x^2 - 4 = 0 d x^2 - 5x + 4 = 0
    1. answers icon 1 answer
  2. Which equation has only one distinct solution?A: x^2 + 4x + 4 = 0 B: x^2 + 5x + 4 = 0 C: x^2 - 4 = 0 D: x^2 - 5x + 4 =0
    1. answers icon 1 answer
  3. In which sentence does the word distinct make sense?The assembly line produced a serious of identical toys, each distinct for
    1. answers icon 3 answers
    1. answers icon 1 answer
more similar questions