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: Apply the quadratic formula
The given quadratic equation is:\[x^2 - 5x + 6 = 0\]We will solve for \( x \) using factorization.
Step 2: Factor the quadratic expression
Identify two numbers that multiply to 6 (the constant term) and add up to -5 (the coefficient of \( x \)).These numbers are -2 and -3, as:\[-2 \times -3 = 6 \quad \text{and} \quad -2 + (-3) = -5\]The factored form of the quadratic equation is:\[(x - 2)(x - 3) = 0\]
Step 3: Determine the roots
Equate each factor to zero:\[x - 2 = 0 \quad \text{or} \quad x - 3 = 0\]Solving these yields:\[x = 2 \quad \text{or} \quad x = 3\]
Answer:
The roots of the equation are \( x = 2 \) and \( x = 3 \). Thus, the correct answer is option (1).