I have the following 5th degree Polynomial Equation in **complex wave velocity** w(tauT, tauq) as a function of real parameters taoT and tauq:

    [1+(c2^2/c1^2) w^2][1+k taoT c2 w+(c2 d/ k) w (1+ k taoq c2 w+(1/2) k^2 taoq^2 c2^2 w^2)]+(e c2 d/ k) w [1+k taoq c2 w+(1/2) k^2 taoq^2 c2^2 w^2] = 0;

The parameters are given as:

    c1=4631.0; c2=2280.1; d=8066.8; e=0.0168; k=1; 

I want the following two plots:
[![enter image description here][1]][1]

The range for both of taoT and Taoq is: 

    [10^-10, 10^-1]

Also, **marked the extremum values and points** if possible on both the graphs.
Can anyone please help me for my research. I am in basic level in learning Mathematica 11.0. Please help me Sir/Madam.

Thank you very much.


    

   

    


  [1]: https://i.sstatic.net/fb8Vw.jpg