Question

$t^4 - 4*t^3 - 14*t^2 + 36*t + 45 textless 0$

Answer 1

t³(t-3)-t²(t-3)-17t(t-3)-15(t-3)<0
(t-3)(t³-t²-17t-15)<0
(t-3)[t²(t+3)-4t(t+3)-5(t+3)]<0
(t-3)(t+3)(t²-4t-5)<0
(t-3)(t+3)[t(t+1)-5(t+1)]<0
(t-3)(t+3)(t+1)(t-5)<0
t=3  t=-3  t=-1  t=5
         +                _                  +                  _                  +
----------(-3)------------(-1)-----------(3)--------------(5)-----------------
t∈(-3;-1) U (3;5)