What is the product of the roots for the quadratic equation \(x^2 - 3x + 2 = 0\)?

To determine the product of the roots of the quadratic equation (x^2 - 3x + 2 = 0), we can utilize Vieta’s formulas. Vieta's formulas provide a relationship between the coefficients of the polynomial and its roots.

For a standard quadratic in the form (ax^2 + bx + c = 0), where (a), (b), and (c) are constants, the product of the roots ((r_1) and (r_2)) can be calculated using the formula:

[

r_1 \cdot r_2 = \frac{c}{a}

]

In this equation, (a) is the coefficient of (x^2), and (c) is the constant term. For the given equation (x^2 - 3x + 2), we can identify the values as follows:

• (a = 1)

• (b = -3)

• (c = 2)

Using Vieta's formula, the product of the roots is:

[

r_1 \cdot r_2 = \frac{2}{1} = 2