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Find the roots of the equation 4x^2 - 12x + 9 = 0.

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Question: Find the roots of the equation 4x^2 - 12x + 9 = 0.

Options:

  1. x = 1.5
  2. x = 3
  3. x = 0
  4. x = -3

Correct Answer: x = 3

Solution: 

Factoring gives (2x - 3)(2x - 3) = 0. Thus, x = 3.

Find the roots of the equation 4x^2 - 12x + 9 = 0.

Practice Questions

Q1
Find the roots of the equation 4x^2 - 12x + 9 = 0.
  1. x = 1.5
  2. x = 3
  3. x = 0
  4. x = -3

Questions & Step-by-Step Solutions

Find the roots of the equation 4x^2 - 12x + 9 = 0.
  • 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 equation using these numbers: 4x^2 - 6x - 6x + 9 = 0.
  • Step 5: Group the terms: (4x^2 - 6x) + (-6x + 9) = 0.
  • Step 6: Factor out common terms: 2x(2x - 3) - 3(2x - 3) = 0.
  • Step 7: 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, the root is x = 3/2.
  • Quadratic Equations – Understanding how to solve quadratic equations using factoring, the quadratic formula, or completing the square.
  • Factoring – Recognizing how to factor a quadratic expression correctly and understanding the implications of repeated roots.
  • Roots of Equations – Identifying the roots of a quadratic equation and understanding their significance in the context of the graph of the equation.
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