The profit of a football club after a takeover is modeled by p(t)=tE3-14tE2+20t+120, where t is the number of years after the takeover. In which years was the club making a loss?

Answer 1

you want
t^3 - 14t^2 + 20t + 12 < 0
This has no rational roots, but it does have zeroes at
t = -0.45, 2.16, 12.29
From what you know about the shape of cubic curves, you know that
p(t) < 0 for 2.16 < t < 12.29
so the team took a loss in years 3-12