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For the quadratic equation x^2 + 2x + 1 = 0, what is the nature of the roots?

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Question: For the quadratic equation x^2 + 2x + 1 = 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, indicating that the roots are real and equal.

For the quadratic equation x^2 + 2x + 1 = 0, what is the nature of the roots?

Practice Questions

Q1
For the quadratic equation x^2 + 2x + 1 = 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 + 2x + 1 = 0, what is the nature of the roots?
  • Step 1: Identify the quadratic equation, which is in the form ax^2 + bx + c. Here, a = 1, b = 2, and c = 1.
  • 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 = (2)^2 - 4(1)(1).
  • Step 4: Simplify the calculation: D = 4 - 4 = 0.
  • Step 5: Analyze the value of the discriminant. Since D = 0, it indicates that 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, given by D = b^2 - 4ac, which 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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