The equation `x^(2) + px +q =0` has two roots ` alpha, beta` then
Choose the correct answer :
(1) The equation ` qx^(2) +(2q -p^(2))x +q` has roots
` (1) alpha /beta , beta/alpha ` (2) `1/alpha ,1/beta`
` (3) alpha^(2), beta^(2)` (4) None of these
(2) The equation whose roots are `1/alpha , 1/beta ` is
`(1) px^(2) + qx + 1 =0` (2) `qx^(2) +px +1 =0`
(3)` x^(2) + qx + p =0 `
(4) `qx^(2) +x+ p =0`
3. the values of p and q when roots are -1,2
(1) p = -1 , q = -2 (2) p =-1 , q =2
(3) p=1 , q = -2 (4) None of these

Explanation

To solve the given problem step by step, let's break it down into the three parts as presented in the question.

### Part 1: Finding the roots of the equation \( qx^2 + (2q - p^2)x + q = 0 \)

1. **Identify the roots of the original equation**:
The original equation is \( x^2 + px + q = 0 \) with roots \( \alpha \) and \( \beta \).
From Vieta's formulas, we know:
- Sum of the roots: \( \alpha + \beta = -p \)
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