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The quadratic equation x^2 + 4x + 4 = 0 has:

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Question: The quadratic equation x^2 + 4x + 4 = 0 has:

Options:

  1. Two distinct real roots
  2. One real root
  3. No real roots
  4. Infinitely many roots

Correct Answer: One real root

Solution: 

The discriminant is 0, indicating one real root (a repeated root).

The quadratic equation x^2 + 4x + 4 = 0 has:

Practice Questions

Q1
The quadratic equation x^2 + 4x + 4 = 0 has:
  1. Two distinct real roots
  2. One real root
  3. No real roots
  4. Infinitely many roots

Questions & Step-by-Step Solutions

The quadratic equation x^2 + 4x + 4 = 0 has:
  • Step 1: Identify the quadratic equation, which is in the form ax^2 + bx + c. Here, a = 1, b = 4, and c = 4.
  • Step 2: Calculate the discriminant using the formula D = b^2 - 4ac.
  • Step 3: Substitute the values of a, b, and c into the discriminant formula: D = (4)^2 - 4(1)(4).
  • Step 4: Simplify the calculation: D = 16 - 16 = 0.
  • Step 5: Interpret the result: Since the discriminant is 0, this means there is one real root (a repeated root).
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