Find the sum of the zeroes of the quadratic polynomial `x^2 + 2x + 3.`

Answer

To find the sum of the zeroes of the quadratic polynomial \( x^2 + 2x + 3 \), we can follow these steps:

### Step 1: Identify the coefficients
The general form of a quadratic polynomial is given by:
\[ ax^2 + bx + c \]
For the polynomial \( x^2 + 2x + 3 \), we can identify the coefficients as follows:
- \( a = 1 \)
- \( b = 2 \)
- \( c = 3 \)

### Step 2: Use the formula for the sum of the zeroes
The sum of the zeroes (roots) of a quadratic polynomial can be calculated using the formula:
\[ \text{Sum of the zeroes} = -\frac{b}{a} \]

### Step 3: Substitute the values of \( a \) and \( b \)
Now, substituting the values we identified:
\[ \text{Sum of the zeroes} = -\frac{2}{1} \]

### Step 4: Calculate the sum
Calculating the above expression gives:
\[ \text{Sum of the zeroes} = -2 \]

### Final Answer
Thus, the sum of the zeroes of the quadratic polynomial \( x^2 + 2x + 3 \) is:
\[ \boxed{-2} \]

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