If `alpha` and `beta` are the zeros of the quadratic polynomial `f(x)=a x^2+b x+c` , then evaluate: (i) `beta/(aalpha+b)+alpha/(abeta+b)` (ii) `a((alpha^2)/beta+(beta^2)/alpha)+b(alpha/beta+beta/alpha)`

Explanation

To solve the given problem, we need to evaluate two expressions involving the roots (zeros) of the quadratic polynomial \( f(x) = ax^2 + bx + c \), where the roots are denoted as \( \alpha \) and \( \beta \).

### Given:
1. The roots \( \alpha \) and \( \beta \) satisfy:
- \( \alpha + \beta = -\frac{b}{a} \) (sum of the roots)
- \( \alpha \beta = \frac{c}{a} \) (product of the roots)

### (i) Evaluate \( \frac{\beta}{a\alpha + b} + \frac{\alpha}{a\beta + b} \)
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