What expression represents the sum of the roots of the polynomial \( x^2 - 8x + 15 \)?

What expression represents the sum of the roots of the polynomial \( x^2 - 8x + 15 \)?

• A. 7
• B. 8
• C. 9
• D. 10

Answer: (B)

To find the sum of the roots of the polynomial \( x^2 - 8x + 15 \), we can use Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots. For a quadratic polynomial of the form \( ax^2 + bx + c \), the sum of the roots is given by \( -\frac{b}{a} \). In the polynomial \( x^2 - 8x + 15 \): - The coefficient \( a \) (for \( x^2 \)) is 1, - The coefficient \( b \) (for \( x \)) is -8. Using Vieta's formula, the sum of the roots can be calculated as follows: \[ \text{Sum of roots} = -\frac{b}{a} = -\frac{-8}{1} = 8. \] Thus, the expression that represents the sum of the roots of the polynomial is 8, making it the correct answer. Understanding this concept is fundamental to working with polynomial equations and helps in deriving various properties of the roots quickly.

To find the sum of the roots of the polynomial ( x^2 - 8x + 15 ), we can use Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots. For a quadratic polynomial of the form ( ax^2 + bx + c ), the sum of the roots is given by ( -\frac{b}{a} ).

In the polynomial ( x^2 - 8x + 15 ):

• The coefficient ( a ) (for ( x^2 )) is 1,

• The coefficient ( b ) (for ( x )) is -8.

Using Vieta's formula, the sum of the roots can be calculated as follows:

[

\text{Sum of roots} = -\frac{b}{a} = -\frac{-8}{1} = 8.

]

Thus, the expression that represents the sum of the roots of the polynomial is 8, making it the correct answer. Understanding this concept is fundamental to working with polynomial equations and helps in deriving various properties of the roots quickly.