If `alpha` and `beta` are zeros of `p(x) = x^2 + x - 1`, then find `alpha^(2)beta + alphabeta^(2)`.

Answer

To solve the problem, we need to find the value of \( \alpha^2 \beta + \alpha \beta^2 \) given that \( \alpha \) and \( \beta \) are the zeros of the polynomial \( p(x) = x^2 + x - 1 \).

### Step-by-Step Solution:

1. **Identify the coefficients of the polynomial**:
The polynomial is given as \( p(x) = x^2 + x - 1 \). Here, we can identify:
- \( a = 1 \)
- \( b = 1 \)
- \( c = -1 \)

2. **Use Vieta's formulas to find the sum and product of the roots**:
According to Vieta's formulas:
- The sum of the roots \( \alpha + \beta = -\frac{b}{a} = -\frac{1}{1} = -1 \)
- The product of the roots \( \alpha \beta = \frac{c}{a} = \frac{-1}{1} = -1 \)

3. **Rewrite the expression \( \alpha^2 \beta + \alpha \beta^2 \)**:
We can factor the expression:
\[ \alpha^2 \beta + \alpha \beta^2 = \alpha \beta (\alpha + \beta) \]

4. **Substitute the values of \( \alpha + \beta \) and \( \alpha \beta \)**:
From the previous steps, we have:
- \( \alpha + \beta = -1 \)
- \( \alpha \beta = -1 \)

Substituting these values into the factored expression:
\[ \alpha^2 \beta + \alpha \beta^2 = \alpha \beta (\alpha + \beta) = (-1)(-1) = 1 \]

5. **Conclusion**:
Thus, the value of \( \alpha^2 \beta + \alpha \beta^2 \) is \( 1 \).

### Final Answer:
\[ \alpha^2 \beta + \alpha \beta^2 = 1 \]