If `p(x) = ax^(2) + bx + c`, then `-b/a` is equal to

Options

A. 0
B. 1
C. product of zeroes
D. sum of zeroes

Answer

To solve the question, we need to understand the relationship between the coefficients of a quadratic polynomial and its roots. The polynomial given is:

\[ p(x) = ax^2 + bx + c \]

We want to find out what \(-\frac{b}{a}\) is equal to.

### Step-by-step Solution:

1. **Identify the quadratic polynomial**:
The polynomial is given as \( p(x) = ax^2 + bx + c \).

2. **Recall the sum of the roots formula**:
For a quadratic polynomial of the form \( ax^2 + bx + c \), the sum of the roots (let's denote the roots as \( r_1 \) and \( r_2 \)) can be calculated using the formula:
\[ r_1 + r_2 = -\frac{b}{a} \]

3. **Apply the formula**:
From the formula, we directly see that \(-\frac{b}{a}\) represents the sum of the roots of the polynomial \( p(x) \).

4. **Conclusion**:
Therefore, \(-\frac{b}{a}\) is equal to the sum of the roots of the quadratic equation \( ax^2 + bx + c \).

### Final Answer:
\(-\frac{b}{a}\) is equal to the sum of the roots of the polynomial.