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What are the roots of the equation x^2 - 5x + 6 = 0?

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Question: What are the roots of the equation x^2 - 5x + 6 = 0?

Options:

  1. 1 and 6
  2. 2 and 3
  3. 3 and 4
  4. 0 and 6

Correct Answer: 2 and 3

Solution: 

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

What are the roots of the equation x^2 - 5x + 6 = 0?

Practice Questions

Q1
What are the roots of the equation x^2 - 5x + 6 = 0?
  1. 1 and 6
  2. 2 and 3
  3. 3 and 4
  4. 0 and 6

Questions & Step-by-Step Solutions

What are the roots of the equation x^2 - 5x + 6 = 0?
Correct Answer: x = 2 and x = 3
  • Step 1: Start with the equation x^2 - 5x + 6 = 0.
  • Step 2: Look for two numbers that multiply to 6 (the last number) and add up to -5 (the middle number).
  • 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.
  • Factoring – Recognizing how to factor a quadratic expression into two binomials.
  • Roots of Equations – Finding the values of x that satisfy the equation.
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