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Find the roots of the equation x^2 - 8x + 16 = 0.

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Question: Find the roots of the equation x^2 - 8x + 16 = 0.

Options:

  1. x = 4
  2. x = -4
  3. x = 8
  4. x = 0

Correct Answer: x = 4

Solution: 

This is a perfect square: (x - 4)² = 0. Thus, x - 4 = 0, so x = 4.

Find the roots of the equation x^2 - 8x + 16 = 0.

Practice Questions

Q1
Find the roots of the equation x^2 - 8x + 16 = 0.
  1. x = 4
  2. x = -4
  3. x = 8
  4. x = 0

Questions & Step-by-Step Solutions

Find the roots of the equation x^2 - 8x + 16 = 0.
  • Step 1: Start with the equation x^2 - 8x + 16 = 0.
  • Step 2: Recognize that the equation can be factored. Look for two numbers that multiply to 16 and add to -8.
  • Step 3: The numbers -4 and -4 work because -4 * -4 = 16 and -4 + -4 = -8.
  • Step 4: Rewrite the equation as (x - 4)(x - 4) = 0.
  • Step 5: This can be simplified to (x - 4)² = 0.
  • Step 6: To find the roots, set (x - 4) = 0.
  • Step 7: Solve for x by adding 4 to both sides: x = 4.
  • Quadratic Equations – The question tests the ability to solve a quadratic equation using factoring, specifically recognizing perfect squares.
  • Perfect Square Trinomials – The solution involves identifying and rewriting the quadratic as a perfect square, which simplifies finding the roots.
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