If one zero of the quadratic polynomial `x^2 + x - 2` is -2, find the other zero.

Answer

To find the other zero of the quadratic polynomial \( x^2 + x - 2 \) given that one zero is \( -2 \), we can follow these steps:

### Step 1: Identify the given zero
We know that one zero of the polynomial is \( \alpha = -2 \).

### Step 2: Use the relationship between the zeros
For a quadratic polynomial of the form \( ax^2 + bx + c \), the sum of the zeros \( \alpha + \beta \) can be calculated using the formula:
\[ \alpha + \beta = -\frac{b}{a} \]
where \( a \) is the coefficient of \( x^2 \) and \( b \) is the coefficient of \( x \).

### Step 3: Substitute the values
In our polynomial \( x^2 + x - 2 \):
- \( a = 1 \)
- \( b = 1 \)

Now, substituting these values into the formula:
\[ \alpha + \beta = -\frac{1}{1} = -1 \]

### Step 4: Substitute the known zero
We already know \( \alpha = -2 \). Now, substituting this into the sum of zeros equation:
\[ -2 + \beta = -1 \]

### Step 5: Solve for the other zero
To find \( \beta \), we can rearrange the equation:
\[ \beta = -1 + 2 \]
\[ \beta = 1 \]

### Conclusion
Thus, the other zero \( \beta \) is \( 1 \).