If `alpha and beta` are the zeros of the polynomial `f(x)=2x^2+5x+k` satisfying the relation `alpha^2+beta^2+alphabeta=(21)/4`, then find the value of `k` for this to be possible.

Explanation

To find the value of \( k \) for the polynomial \( f(x) = 2x^2 + 5x + k \) given that the zeros \( \alpha \) and \( \beta \) satisfy the relation \( \alpha^2 + \beta^2 + \alpha\beta = \frac{21}{4} \), we can follow these steps:

### Step 1: Identify the relationships between the zeros
From Vieta's formulas, we know:
- The sum of the zeros \( \alpha + \beta = -\frac{b}{a} = -\frac{5}{2} \)
- The product of the zeros \( \alpha \beta = \frac{c}{a} = \frac{k}{2} \)

### Step 2: Express \( \alpha^2 + \beta^2 \) in terms of \( \alpha + \beta \) and \( \alpha \beta \)
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