Analyse a parameterised polynomial family

Use \(a\) in place of \(x\) at every step; the input and the family value need not be kept separate

Changing \(a\) changes only the label of the member; all polynomial outputs and coefficients stay unchanged

The difference between the coefficients of \(x^{3}\) and \(x^{2}\) remains \(-\frac{3}{4}\), because both coefficients receive the same parameter contribution

The roots and coefficients found for the member with \(a=\frac{4}{3}\) can be used unchanged for every other member