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The quadratic equation x^2 - 6x + 9 = 0 has how many distinct real roots?

Practice Questions

Q1
The quadratic equation x^2 - 6x + 9 = 0 has how many distinct real roots?
  1. 0
  2. 1
  3. 2
  4. Infinite

Questions & Step-by-Step Solutions

The quadratic equation x^2 - 6x + 9 = 0 has how many distinct real roots?
Correct Answer: 1
  • Step 1: Identify the quadratic equation, which is in the form ax^2 + bx + c. Here, a = 1, b = -6, and c = 9.
  • 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 = (-6)^2 - 4(1)(9).
  • Step 4: Calculate (-6)^2, which is 36.
  • Step 5: Calculate 4(1)(9), which is 36.
  • Step 6: Now, subtract the two results: D = 36 - 36 = 0.
  • Step 7: Interpret the discriminant: If D = 0, it means there is exactly one distinct real root.
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