If roots of the equation `a x^2+b x+c=0` are `alpha and beta` , find the equation whose roots are `1/alpha,1/beta` (ii) `-alpha,-beta` (iii) `(1-alpha)/(1+alpha),(1-beta)/(1+beta)`

Explanation

To solve the problem, we will find the equations whose roots are transformations of the roots of the original quadratic equation \( ax^2 + bx + c = 0 \) where the roots are \( \alpha \) and \( \beta \).

### Part (i): Finding the equation with roots \( \frac{1}{\alpha} \) and \( \frac{1}{\beta} \)

1. **Let \( y = \frac{1}{\alpha} \)**. Then, \( \alpha = \frac{1}{y} \).
2. Substitute \( \alpha \) into the original equation:
\[
a\left(\frac{1}{y}\right)^2 + b\left(\frac{1}{y}\right) + c = 0
...