Find the sum and product of zeros of the quadratic polynomial `ax^(2) + bx+c`.

Answer

To find the sum and product of the zeros of the quadratic polynomial \( ax^2 + bx + c \), we can follow these steps:

### Step 1: Identify the coefficients
The given quadratic polynomial is in the form \( ax^2 + bx + c \). Here, the coefficients are:
- \( a \) (coefficient of \( x^2 \))
- \( b \) (coefficient of \( x \))
- \( c \) (constant term)

### Step 2: Use the formulas for sum and product of zeros
For any quadratic polynomial of the form \( ax^2 + bx + c \), the sum and product of its zeros (roots) can be calculated using the following formulas:
- **Sum of the zeros** \( \alpha + \beta = -\frac{b}{a} \)
- **Product of the zeros** \( \alpha \beta = \frac{c}{a} \)

### Step 3: Calculate the sum of the zeros
Using the formula for the sum of the zeros:
\[ \text{Sum of zeros} = -\frac{b}{a} \]

### Step 4: Calculate the product of the zeros
Using the formula for the product of the zeros:
\[ \text{Product of zeros} = \frac{c}{a} \]

### Final Result
Thus, the sum and product of the zeros of the quadratic polynomial \( ax^2 + bx + c \) are:
- **Sum of zeros**: \( -\frac{b}{a} \)
- **Product of zeros**: \( \frac{c}{a} \)

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