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The quadratic equation x^2 - 6x + 9 = 0 can be expressed as which of the followi

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Question: The quadratic equation x^2 - 6x + 9 = 0 can be expressed as which of the following? (2021)

Options:

  1. (x - 3)^2 = 0
  2. (x + 3)^2 = 0
  3. (x - 2)(x - 4) = 0
  4. (x + 2)(x + 4) = 0

Correct Answer: (x - 3)^2 = 0

Exam Year: 2021

Solution: 

The equation can be factored as (x - 3)(x - 3) = 0, or (x - 3)^2 = 0.

The quadratic equation x^2 - 6x + 9 = 0 can be expressed as which of the followi

Practice Questions

Q1
The quadratic equation x^2 - 6x + 9 = 0 can be expressed as which of the following? (2021)
  1. (x - 3)^2 = 0
  2. (x + 3)^2 = 0
  3. (x - 2)(x - 4) = 0
  4. (x + 2)(x + 4) = 0

Questions & Step-by-Step Solutions

The quadratic equation x^2 - 6x + 9 = 0 can be expressed as which of the following? (2021)
  • Step 1: Start with the quadratic equation x^2 - 6x + 9 = 0.
  • Step 2: Look for two numbers that multiply to 9 (the constant term) and add up to -6 (the coefficient of x).
  • Step 3: The numbers -3 and -3 work because -3 * -3 = 9 and -3 + -3 = -6.
  • Step 4: Rewrite the equation using these numbers: (x - 3)(x - 3) = 0.
  • Step 5: This can also be written as (x - 3)^2 = 0.
  • Factoring Quadratic Equations – Understanding how to factor a quadratic equation into its binomial components.
  • Identifying Perfect Squares – Recognizing that the quadratic can be expressed as a perfect square.
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