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What are the solutions to the quadratic equation x^2 + 4x + 4 = 0?

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Question: What are the solutions to the quadratic equation x^2 + 4x + 4 = 0?

Options:

  1. x = -2, -2
  2. x = 2, 2
  3. x = -4, 0
  4. x = 0, 4

Correct Answer: x = -2, -2

Solution: 

Step 1: Factor the equation: (x + 2)(x + 2) = 0. Step 2: Set the factor to zero: x + 2 = 0. Step 3: Solution is x = -2 (double root).

What are the solutions to the quadratic equation x^2 + 4x + 4 = 0?

Practice Questions

Q1
What are the solutions to the quadratic equation x^2 + 4x + 4 = 0?
  1. x = -2, -2
  2. x = 2, 2
  3. x = -4, 0
  4. x = 0, 4

Questions & Step-by-Step Solutions

What are the solutions to the quadratic equation x^2 + 4x + 4 = 0?
Correct Answer: x = -2
  • Step 1: Factor the equation x^2 + 4x + 4. This can be written as (x + 2)(x + 2) because both factors are the same.
  • Step 2: Set the factor equal to zero. Since we have (x + 2)(x + 2) = 0, we can set one of the factors to zero: x + 2 = 0.
  • Step 3: Solve for x. To find x, subtract 2 from both sides: x = -2.
  • Step 4: Identify the type of root. Since we got the same solution from both factors, x = -2 is a double root.
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