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In the quadratic equation x² + 6x + 9 = 0, what is the nature of the roots?

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Question: In the quadratic equation x² + 6x + 9 = 0, what is the nature of the roots?

Options:

  1. Real and distinct
  2. Real and equal
  3. Complex
  4. Imaginary

Correct Answer: Real and equal

Solution: 

The discriminant is 0 (b² - 4ac = 0), indicating that the roots are real and equal.

In the quadratic equation x² + 6x + 9 = 0, what is the nature of the roots?

Practice Questions

Q1
In the quadratic equation x² + 6x + 9 = 0, what is the nature of the roots?
  1. Real and distinct
  2. Real and equal
  3. Complex
  4. Imaginary

Questions & Step-by-Step Solutions

In the quadratic equation x² + 6x + 9 = 0, what is the nature of the roots?
  • Step 1: Identify the coefficients in the quadratic equation x² + 6x + 9 = 0. Here, a = 1, b = 6, and c = 9.
  • Step 2: Use the formula for the discriminant, which is b² - 4ac.
  • Step 3: Calculate b²: 6² = 36.
  • Step 4: Calculate 4ac: 4 * 1 * 9 = 36.
  • Step 5: Subtract the two results: 36 - 36 = 0.
  • Step 6: Since the discriminant is 0, this means the roots are real and equal.
  • Quadratic Equation – A polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants.
  • Discriminant – A value calculated from the coefficients of a quadratic equation (b² - 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.
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