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The quadratic equation x^2 - 4x + 4 = 0 can be expressed in which of the followi

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Question: The quadratic equation x^2 - 4x + 4 = 0 can be expressed in which of the following forms? (2022)

Options:

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

Correct Answer: (x - 2)^2

Exam Year: 2022

Solution: 

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

The quadratic equation x^2 - 4x + 4 = 0 can be expressed in which of the followi

Practice Questions

Q1
The quadratic equation x^2 - 4x + 4 = 0 can be expressed in which of the following forms? (2022)
  1. (x - 2)^2
  2. (x + 2)^2
  3. (x - 4)^2
  4. (x + 4)^2

Questions & Step-by-Step Solutions

The quadratic equation x^2 - 4x + 4 = 0 can be expressed in which of the following forms? (2022)
  • Step 1: Start with the quadratic equation: x^2 - 4x + 4 = 0.
  • Step 2: Look for two numbers that multiply to 4 (the constant term) and add to -4 (the coefficient of x).
  • Step 3: The numbers -2 and -2 work because -2 * -2 = 4 and -2 + -2 = -4.
  • Step 4: Rewrite the equation using these numbers: (x - 2)(x - 2) = 0.
  • Step 5: Recognize that (x - 2)(x - 2) can be written as (x - 2)^2.
  • Step 6: Therefore, the quadratic equation can be expressed as (x - 2)^2 = 0.
  • Factoring Quadratic Equations – The process of rewriting a quadratic equation in the form of a product of its linear factors.
  • Identifying Perfect Squares – Recognizing that the quadratic can be expressed as a square of a binomial.
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