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What are the roots of the polynomial x^2 - 5x + 6?

Practice Questions

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

Questions & Step-by-Step Solutions

What are the roots of the polynomial x^2 - 5x + 6?
  • Step 1: Write down the polynomial you want to find the roots for: x^2 - 5x + 6.
  • Step 2: Look for two numbers that multiply to the constant term (6) and add up to the coefficient of the x term (-5).
  • Step 3: The two numbers that work are -2 and -3 because (-2) * (-3) = 6 and (-2) + (-3) = -5.
  • Step 4: Rewrite the polynomial using these two numbers: x^2 - 5x + 6 = (x - 2)(x - 3).
  • Step 5: Set each factor equal to zero: x - 2 = 0 and x - 3 = 0.
  • Step 6: Solve each equation: For x - 2 = 0, x = 2. For x - 3 = 0, x = 3.
  • Step 7: The roots of the polynomial are x = 2 and x = 3.
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