Answer the following independent cases, each relating to the interpretation of roots in measurement contexts.
(a) A quadratic equation x2−5x−36=0 arises while calculating the length (in metres) of a garden. The equation has roots x=9 and x=−4. Which value of x should be accepted? Give a reason.
(b) While analysing the time taken (in hours) for a road journey, a student arrives at the equation t2−5t+6=0. Explain whether each of its roots is admissible in the context of time.
(c) In attempting to solve a geometry problem, a learner obtains the equation p2+8p+20=0, where p represents a length in centimetres. Show that no real value of p satisfies this equation and interpret the practical meaning of this result.