Question

The profit of a football club after a takeover is modeled by p(t)=t^3-14t^2+20t+120,where t is the number of years after the take over, in which years was the club making a loss ?

Answer 1

When looking at the following expression, we can tell that it has no rational roots. However, it does have zeros at:

t = -0.45, 2.16, 12.29.

When thinking of the cubic curves you know that p(t) < 0 for 2.16 < t < 12.29. Meaning the team took a loss in years 3-12.

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