Conquer the College Math Placement Challenge 2026 – Step Up and Shine!

The product of the roots of a quadratic equation can be determined using Vieta's formulas, which relate the coefficients of the polynomial to sums and products of its roots. For a quadratic equation in the standard form \( ax^2 + bx + c = 0 \), Vieta's formulas tell us that the product of the roots \( r_1 \) and \( r_2 \) is given by \( \frac{c}{a} \).

In the equation \( x^2 - 5x + 6 = 0 \), the coefficients \( a \), \( b \), and \( c \) are as follows:

- \( a = 1 \)

- \( b = -5 \)

- \( c = 6 \)

Applying Vieta's formula, the product of the roots \( r_1 \times r_2 \) is calculated as:

\[

r_1 \times r_2 = \frac{c}{a} = \frac{6}{1} = 6.

\]

Thus, the product of the roots of the equation \( x^2 - 5x + 6 = 0 \) is indeed 6. This is why the correct answer is