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

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

• A. 6
• B. 5
• C. 1
• D. 0

Answer: (B)

To find the sum of the roots of the quadratic equation \(x^2 - 5x + 6 = 0\), we can use the properties of quadratic equations as defined by Vieta's formulas. For a standard quadratic equation of the form \(ax^2 + bx + c = 0\), the sum of the roots is given by the formula \(-\frac{b}{a}\). In this specific equation, we identify \(a = 1\), \(b = -5\), and \(c = 6\). Applying Vieta's formula, we calculate the sum of the roots as follows: \[ \text{Sum of the roots} = -\frac{-5}{1} = \frac{5}{1} = 5. \] Thus, the sum of the roots of the given quadratic equation is indeed 5. This confirms that the answer is correct.

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

In this specific equation, we identify (a = 1), (b = -5), and (c = 6). Applying Vieta's formula, we calculate the sum of the roots as follows:

[

\text{Sum of the roots} = -\frac{-5}{1} = \frac{5}{1} = 5.

]

Thus, the sum of the roots of the given quadratic equation is indeed 5. This confirms that the answer is correct.