Can a 6th degree equation be solved by hand without a CAS?

[Mr Davis 97]

I have the equation $2t^{6} + 13t^{4} - 36 = 0$. How can I solve this for the real roots without using a CAS? That is, by hand?

 

[micromass]

First substitute $u=t^2$. Then apply the rational root theorem.

 

[Mark44]

http://en.wikipedia.org/wiki/Rational_root_theorem

 

[Vanadium 50]

After the substitution, you might want to graph it.