What is the product of the roots of the polynomial \( x^2 - 5x + 6 \)?

What is the product of the roots of the polynomial \( x^2 - 5x + 6 \)?

• A. 5
• B. 6
• C. 7
• D. 8

Answer: (B)

To determine the product of the roots of the polynomial \( x^2 - 5x + 6 \), we can use Vieta's formulas. According to Vieta's, for a quadratic equation of the form \( ax^2 + bx + c = 0 \), the sum of the roots is given by \( -\frac{b}{a} \) and the product of the roots is given by \( \frac{c}{a} \). In the polynomial \( x^2 - 5x + 6 \): - The coefficient \( a \) (the coefficient in front of \( x^2 \)) is 1. - The coefficient \( b \) (the coefficient in front of \( x \)) is -5. - The constant term \( c \) is 6. To find the product of the roots, we apply the formula: \[ \text{Product of the roots} = \frac{c}{a} = \frac{6}{1} = 6. \] Thus, the product of the roots is 6, confirming that the correct answer is indeed 6. This reflects the fundamental relationship in quadratic equations that relates coefficients to the properties of their roots

To determine the product of the roots of the polynomial ( x^2 - 5x + 6 ), we can use Vieta's formulas. According to Vieta's, for a quadratic equation of the form ( ax^2 + bx + c = 0 ), the sum of the roots is given by ( -\frac{b}{a} ) and the product of the roots is given by ( \frac{c}{a} ).

In the polynomial ( x^2 - 5x + 6 ):

• The coefficient ( a ) (the coefficient in front of ( x^2 )) is 1.

• The coefficient ( b ) (the coefficient in front of ( x )) is -5.

• The constant term ( c ) is 6.

To find the product of the roots, we apply the formula:

[

\text{Product of the roots} = \frac{c}{a} = \frac{6}{1} = 6.

]

Thus, the product of the roots is 6, confirming that the correct answer is indeed 6. This reflects the fundamental relationship in quadratic equations that relates coefficients to the properties of their roots