Question

Find the roots of the quadratic equation $ x^2 - 5x + 6 = 0 $.

• A. \( x = 2, 3 \)
• B. \( x = 1, 6 \)
• C. \( x = -2, 3 \)
• D. \( x = -1, -6 \)

Hint:

Remember: When factorizing a quadratic equation, look for two numbers whose product equals the constant term and whose sum equals the middle term's coefficient.

Answer 1

The Correct Option is A

Step 1: Use the quadratic formula
The given quadratic equation is: \[ x^2 - 5x + 6 = 0 \] To solve for \( x \), we will use the factorization method.
Step 2: Factorize the quadratic expression
We need to find two numbers whose product is 6 (the constant term) and whose sum is -5 (the coefficient of \( x \)). The numbers are -2 and -3 because: \[ -2 \times -3 = 6 \quad \text{and} \quad -2 + (-3) = -5 \] Thus, the factorization of the quadratic equation is: \[ (x - 2)(x - 3) = 0 \]
Step 3: Solve for the roots
Set each factor equal to zero: \[ x - 2 = 0 \quad \text{or} \quad x - 3 = 0 \] Solving these equations gives: \[ x = 2 \quad \text{or} \quad x = 3 \]
Answer:
Therefore, the roots of the equation are \( x = 2 \) and \( x = 3 \). So, the correct answer is option (1).