My Learning Cart
?
Categories
Account

For the quadratic equation x^2 + 4x + 4 = 0, what is the nature of the roots?

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: For the quadratic equation x^2 + 4x + 4 = 0, what is the nature of the roots?

Options:

  1. Real and distinct
  2. Real and equal
  3. Complex
  4. None of the above

Correct Answer: Real and equal

Solution: 

The discriminant is 0 (b^2 - 4ac = 16 - 16 = 0), indicating real and equal roots.

For the quadratic equation x^2 + 4x + 4 = 0, what is the nature of the roots?

Practice Questions

Q1
For the quadratic equation x^2 + 4x + 4 = 0, what is the nature of the roots?
  1. Real and distinct
  2. Real and equal
  3. Complex
  4. None of the above

Questions & Step-by-Step Solutions

For the quadratic equation x^2 + 4x + 4 = 0, what is the nature of the roots?
  • Step 1: Identify the coefficients in the quadratic equation x^2 + 4x + 4 = 0. Here, a = 1, b = 4, and c = 4.
  • Step 2: Use the formula for the discriminant, which is b^2 - 4ac.
  • Step 3: Calculate b^2: 4^2 = 16.
  • Step 4: Calculate 4ac: 4 * 1 * 4 = 16.
  • Step 5: Subtract the two results: 16 - 16 = 0.
  • Step 6: Interpret the result: Since the discriminant is 0, this means the roots are real and equal.
  • Quadratic Equation – A polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.
  • Discriminant – A value calculated from the coefficients of a quadratic equation (b^2 - 4ac) that determines the nature of the roots.
  • Nature of Roots – The classification of the roots of a quadratic equation as real and distinct, real and equal, or complex.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks