If both the zeros of the quadratic polynomial `ax^2 + bx + c` are equal and opposite in sign, then find the value of b.

Answer

To solve the problem, we need to find the value of \( b \) in the quadratic polynomial \( ax^2 + bx + c \) given that both zeros are equal and opposite in sign.

### Step-by-Step Solution:

1. **Understanding the Zeros**:
Let the zeros of the polynomial be \( \alpha \) and \( \beta \). According to the problem, the zeros are equal in magnitude but opposite in sign. This means we can express the relationship as:
\[ \beta = -\alpha \]

2. **Sum of the Zeros**:
The sum of the zeros of a quadratic polynomial \( ax^2 + bx + c \) is given by the formula:
\[ \alpha + \beta = -\frac{b}{a} \]
Substituting \( \beta = -\alpha \) into the sum:
\[ \alpha + (-\alpha) = 0 \]
Therefore, we have:
\[ 0 = -\frac{b}{a} \]

3. **Solving for \( b \)**:
From the equation \( 0 = -\frac{b}{a} \), we can multiply both sides by \( a \) (assuming \( a \neq 0 \)):
\[ 0 = -b \]
This implies:
\[ b = 0 \]

### Conclusion:
Thus, the value of \( b \) is \( 0 \).