What is the sum of the roots of the quadratic equation \(x^2 - 5x + 6 = 0\)?

To determine the sum of the roots of the quadratic equation (x^2 - 5x + 6 = 0), you can use the relationship given by Vieta's formulas. For a quadratic equation in the standard form (ax^2 + bx + c = 0), the sum of the roots is given by the formula (-\frac{b}{a}).

In this particular equation:

• The coefficient (a) (the coefficient of (x^2)) is 1.

• The coefficient (b) (the coefficient of (x)) is -5.

Applying Vieta's formula, the sum of the roots is calculated as follows:

[

-\frac{b}{a} = -\frac{-5}{1} = 5

]

Thus, the sum of the roots of the equation (x^2 - 5x + 6 = 0) is indeed 5. This confirms that the correct answer is the option that states 5.