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

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

Options:

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

Correct Answer: x = 2, 3

Solution: 

Step 1: Factor the equation: (x - 2)(x - 3) = 0. Step 2: Set each factor to zero: x - 2 = 0 or x - 3 = 0. Step 3: Solutions are x = 2 and x = 3.

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

Practice Questions

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

Questions & Step-by-Step Solutions

What are the roots of the quadratic equation x^2 - 5x + 6 = 0?
Correct Answer: x = 2 and x = 3
  • Step 1: Factor the equation x^2 - 5x + 6 into two binomials. We look for two numbers that multiply to 6 (the constant term) and add to -5 (the coefficient of x). The numbers are -2 and -3. So, we can write the equation as (x - 2)(x - 3) = 0.
  • Step 2: Set each factor equal to zero. This gives us two equations: x - 2 = 0 and x - 3 = 0.
  • Step 3: Solve each equation. For x - 2 = 0, we add 2 to both sides to get x = 2. For x - 3 = 0, we add 3 to both sides to get x = 3.
  • Step 4: The solutions (or roots) of the quadratic equation are 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.
  • Zero Product Property – Applying the zero product property to find the roots of the equation.
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