What is the product of the roots of the quadratic equation x^2 - 5x + 6 = 0?

What is the product of the roots of the quadratic equation x^2 - 5x + 6 = 0?

• A. 5
• B. 6
• C. 12
• D. 0

Answer: (B)

To find the product of the roots of the quadratic equation \(x^2 - 5x + 6 = 0\), one can use Vieta's formulas, which state that for a quadratic equation in the form \(ax^2 + bx + c = 0\), the sum of the roots is \(-\frac{b}{a}\) and the product of the roots is \(\frac{c}{a}\). In this case, the coefficients are \(a = 1\), \(b = -5\), and \(c = 6\). Applying Vieta's formula for the product of the roots: \[ \text{Product of the roots} = \frac{c}{a} = \frac{6}{1} = 6 \] Thus, the product of the roots of the equation \(x^2 - 5x + 6 = 0\) is indeed 6, which matches the correct answer. Understanding this concept is crucial as it allows for quick calculations regarding the properties of roots in quadratic equations without needing to solve for the roots explicitly.

To find the product of the roots of the quadratic equation (x^2 - 5x + 6 = 0), one can use Vieta's formulas, which state that for a quadratic equation in the form (ax^2 + bx + c = 0), the sum of the roots is (-\frac{b}{a}) and the product of the roots is (\frac{c}{a}).

In this case, the coefficients are (a = 1), (b = -5), and (c = 6). Applying Vieta's formula for the product of the roots:

[

\text{Product of the roots} = \frac{c}{a} = \frac{6}{1} = 6

]

Thus, the product of the roots of the equation (x^2 - 5x + 6 = 0) is indeed 6, which matches the correct answer. Understanding this concept is crucial as it allows for quick calculations regarding the properties of roots in quadratic equations without needing to solve for the roots explicitly.