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Solve for x: 4x^2 - 12x + 9 = 0.

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Question: Solve for x: 4x^2 - 12x + 9 = 0.

Options:

  1. x = 1
  2. x = 3
  3. x = 2
  4. x = 4

Correct Answer: x = 3

Solution: 

This factors to (2x - 3)(2x - 3) = 0, giving the double root x = 3.

Solve for x: 4x^2 - 12x + 9 = 0.

Practice Questions

Q1
Solve for x: 4x^2 - 12x + 9 = 0.
  1. x = 1
  2. x = 3
  3. x = 2
  4. x = 4

Questions & Step-by-Step Solutions

Solve for x: 4x^2 - 12x + 9 = 0.
Correct Answer: x = 3
  • Step 1: Start with the equation 4x^2 - 12x + 9 = 0.
  • Step 2: Look for two numbers that multiply to (4 * 9) = 36 and add to -12.
  • Step 3: The numbers -6 and -6 work because -6 * -6 = 36 and -6 + -6 = -12.
  • Step 4: Rewrite the middle term using these numbers: 4x^2 - 6x - 6x + 9 = 0.
  • Step 5: Group the terms: (4x^2 - 6x) + (-6x + 9) = 0.
  • Step 6: Factor out the common factors: 2x(2x - 3) - 3(2x - 3) = 0.
  • Step 7: Now, factor by grouping: (2x - 3)(2x - 3) = 0.
  • Step 8: Set each factor equal to zero: 2x - 3 = 0.
  • Step 9: Solve for x: 2x = 3, so x = 3/2.
  • Step 10: Since both factors are the same, this is a double root, so x = 3.
  • Quadratic Equations – The question tests the ability to solve a quadratic equation using factoring.
  • Factoring – It assesses the skill of recognizing and applying the factoring method to find roots.
  • Double Roots – The problem involves understanding the concept of double roots in quadratic equations.
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