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

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