BTW,
1. what the hell do you want roots for all those values for?
2. Why not analyze the function a different way?
Ignore the p*t^4 term for a moment and graph the rest of the function
Now, on top of that function, graph p*t^4..... this will look like a parabola, a little flattened near the vertex, with the vertex on the origin... for negative values of p, it will be upside down, for positive values of p, it will be rightside up. The larger the absolute value of p, the more stretched vertically the curve will look. For absolute values less than 1, the curve will look stretched horizontally.
Now, your original function, including the t^4 term, will be the geometric sum of the two curves.
It would be possible in mathematica to write a program to animate the curves as p varied... I don't have a clue how to do it in maple, though, since I never used maple.