10. The quadratic equation \(p x ^ { 2 } + q x + r = 0\) has roots \(\alpha\) and \(\beta\), where \(p , q , r\) are non-zero constants.
- A cubic equation is formed with roots \(\alpha , \beta , \alpha + \beta\).
Find the cubic equation with coefficients expressed in terms of \(p , q , r\).
- Another quadratic equation \(p x ^ { 2 } - q x - r = 0\) has roots \(2 \alpha\) and \(\gamma\).
Show that \(\beta = - 2 \gamma\).