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

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

• A. 4
• B. 5
• C. 6
• D. 7

Answer: (C)

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

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