A quadratic equation obtained while modelling the ages of a father and his son is
x2−8x−192=0,
where x represents the son’s present age in years. The equation has roots 16 and −12.
(i) Explain clearly why the value x=−12 is not an acceptable answer in the given context.
(ii) Using the admissible root, determine the present ages of the father and the son, given that the father is 24 years older than his son.
(iii) State one other contextual reason (apart from a negative value) for which a root obtained from an age-related quadratic equation might be rejected.