You are given that \(p = 2 + \sqrt { 3 }\) and \(q = 2 - \sqrt { 3 }\) are the roots of a quadratic equation. Find \(p + q\) and \(p q\) and hence find the quadratic equation with roots \(x = p\) and \(x = q\).
Solve the quadratic equation \(x ^ { 2 } + 5 x - 7 = 0\) giving the roots exactly.
Show that \(x = 1\) is the only root of the equation \(x ^ { 3 } + 2 x - 3 = 0\).
A quadratic equation \(x ^ { 2 } + r x + s = 0\), where \(r\) and \(s\) are integers, has two roots. One root is \(x = 3 + \sqrt { 5 }\). Without finding \(r\) or \(s\), write down the other root.