If `alpha and beta` are the zeros of the polynomial `f(x)=x^2-5x+k` such that `alpha-beta=1,` find the value of `k`.

Explanation

To find the value of \( k \) in the polynomial \( f(x) = x^2 - 5x + k \) given that the zeros \( \alpha \) and \( \beta \) satisfy \( \alpha - \beta = 1 \), we can follow these steps:

### Step 1: Use the relationship between the roots and coefficients
For a quadratic polynomial \( ax^2 + bx + c \), the sum and product of the roots (zeros) can be expressed as:
- Sum of the roots: \( \alpha + \beta = -\frac{b}{a} \)
- Product of the roots: \( \alpha \beta = \frac{c}{a} \)

In our case:
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