The equation \(5 x ^ { 2 } - 4 x + 2 = 0\) has roots \(\frac { 1 } { p }\) and \(\frac { 1 } { q }\)
Without solving the equation,
show that \(p q = \frac { 5 } { 2 }\)
determine the value of \(p + q\)
Hence, without finding the values of \(p\) and \(q\), determine a quadratic equation with roots
$$\frac { p } { p ^ { 2 } + 1 } \text { and } \frac { q } { q ^ { 2 } + 1 }$$
giving your answer in the form \(a x ^ { 2 } + b x + c = 0\) where \(a , b\) and \(c\) are integers.