Question

If x² − 5x + 6 = 0, what is the sum of the roots?

• A. 3
• B. 4
• C. 5
• D. 6

Hint:

For quadratic equations, use sum of roots = -\frac{b}{a} for quick calculation.

Answer 1

The Correct Option is C

Step-by-step Solution

1. Identify coefficients.
   A quadratic in standard form is a·x² + b·x + c = 0.
   Here, a = 1, b = −5, c = 6.
2. Use Vieta’s formula (sum of roots).
   For a·x² + b·x + c = 0, the sum of roots (α + β) = −b / a.
3. Substitute values.
   α + β = −(−5) / 1 = 5.
4. Cross-check by factoring (optional).
   x² − 5x + 6 = (x − 2)(x − 3) ⇒ roots are 2 and 3.
   Sum = 2 + 3 = 5 ✓

Final Answer

5 (Correct Option)