[tex]2t ^2 + 11t +12 < 0 \\ \\first\ we \ solve: \\2t ^2 + 11t +12 =0 \\ (t+ 4) (2t +3)=0 \\t+4=0 \ \ or \ \2t+3=0 \\t=-4\ \ or \ \ 2t= -3 \\ x=-5\ \ or \ \ t= -\frac{3}{2}=-1.5[/tex]
So we know that the curve is u-shaped and it crosses the t-axis at t=-5 and t= - 1.5 5
The curve is less than zero :
[tex]-4 < t < - 1.5[/tex]