O14-904
> restart:with(linalg):with(plots):
Warning, new definition for norm
Warning, new definition for trace
> p:=2*x^3-x^2-x-3:

> rac:=[solve(p)];

       rac := [3/2, -1/2 + 1/2 I sqrt(3), -1/2 - 1/2 I sqrt(3)]

> q:=diff(p,x):rac1:=[solve(q)];

            rac1 := [1/6 + 1/6 sqrt(7), 1/6 - 1/6 sqrt(7)]

> c:=1/6*sqrt(7);a:=1/6+1/2;b:=sqrt(a^2-c^2);

                           c := 1/6 sqrt(7)


                               a := 2/3


                               b := 1/2

> 
> 

> ellipse:=[1/6+a*cos(t),b*sin(t),t=-Pi..Pi];

       ellipse := [1/6 + 2/3 cos(t), 1/2 sin(t), t = -Pi .. Pi]

> dte1:=(x-3/2)*3^(1/2)/4;dte2:=-(x-3/2)*3^(1/2)/4;dte3:=plot([-.5,s,s=-1..1]):

                    dte1 := 1/4 (x~ - 3/2) sqrt(3)


                   dte2 := - 1/4 (x~ - 3/2) sqrt(3)

> 
> display([plot(ellipse),plot(dte2,x=-1..2),plot(dte1,x=-1..2),dte3]);

>