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Solve the quadratic equation x^2 - 5x + 6 = 0.

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Question: Solve the quadratic equation x^2 - 5x + 6 = 0.

Options:

  1. x = 2, 3
  2. x = 1, 6
  3. x = -2, -3
  4. x = 0, 5

Correct Answer: x = 2, 3

Solution: 

Factor the equation: (x - 2)(x - 3) = 0. Thus, x = 2 or x = 3.

Solve the quadratic equation x^2 - 5x + 6 = 0.

Practice Questions

Q1
Solve the quadratic equation x^2 - 5x + 6 = 0.
  1. x = 2, 3
  2. x = 1, 6
  3. x = -2, -3
  4. x = 0, 5

Questions & Step-by-Step Solutions

Solve the quadratic equation x^2 - 5x + 6 = 0.
  • Step 1: Start with the quadratic equation: x^2 - 5x + 6 = 0.
  • Step 2: Look for two numbers that multiply to 6 (the constant term) and add up to -5 (the coefficient of x).
  • Step 3: The numbers -2 and -3 work because -2 * -3 = 6 and -2 + -3 = -5.
  • Step 4: Rewrite the equation using these numbers: (x - 2)(x - 3) = 0.
  • Step 5: Set each factor equal to zero: x - 2 = 0 and x - 3 = 0.
  • Step 6: Solve for x in each equation: x = 2 and x = 3.
  • 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 into the product of two binomials.
  • Roots of Equations – Finding the values of x that satisfy the equation, known as the roots or solutions.
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