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

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer: (B)

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

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