Express \(4 x ^ { 2 } - 12 x + 11\) in the form \(a ( x + b ) ^ { 2 } + c\).
State the number of real roots of the equation \(4 x ^ { 2 } - 12 x + 11 = 0\).
Explain fully how the value of \(r\) is related to the number of real roots of the equation \(p ( x + q ) ^ { 2 } + r = 0\) where \(p , q\) and \(r\) are real constants and \(p > 0\).