If `alpha, beta` are the zeros of the polynomial `f(x) = x^2 – 3x + 2`, then find `1/alpha + 1/beta`.

Answer

To solve the problem, we need to find \( \frac{1}{\alpha} + \frac{1}{\beta} \) where \( \alpha \) and \( \beta \) are the zeros of the polynomial \( f(x) = x^2 - 3x + 2 \).

### Step-by-step Solution:

1. **Identify the Polynomial**:
We have the polynomial \( f(x) = x^2 - 3x + 2 \).

2. **Set the Polynomial to Zero**:
To find the zeros, we set the polynomial equal to zero:
\[ x^2 - 3x + 2 = 0 \]

3. **Compare with Standard Form**:
The standard form of a quadratic polynomial is \( ax^2 + bx + c = 0 \). Here, we identify:
- \( a = 1 \)
- \( b = -3 \)
- \( c = 2 \)

4. **Calculate the Sum of Roots**:
The sum of the roots \( \alpha + \beta \) can be calculated using the formula:
\[ \alpha + \beta = -\frac{b}{a} = -\frac{-3}{1} = 3 \]

5. **Calculate the Product of Roots**:
The product of the roots \( \alpha \beta \) can be calculated using the formula:
\[ \alpha \beta = \frac{c}{a} = \frac{2}{1} = 2 \]

6. **Find \( \frac{1}{\alpha} + \frac{1}{\beta} \)**:
We can express \( \frac{1}{\alpha} + \frac{1}{\beta} \) in terms of the sum and product of the roots:
\[ \frac{1}{\alpha} + \frac{1}{\beta} = \frac{\beta + \alpha}{\alpha \beta} \]
Substituting the values we found:
\[ \frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha + \beta}{\alpha \beta} = \frac{3}{2} \]

### Final Answer:
\[ \frac{1}{\alpha} + \frac{1}{\beta} = \frac{3}{2} \]