1) Prove that the acute angle whose cosine is 1/10 cannot be trisected with straightedge and compass. ... I worked it out and at the end found out that , if I can prove that the cubic polynomial 40x3 - 30x -1 has no rational roots, then I am done. Now, is there any way to prove (e.g. divisibility, elementary number theory) that 40x3 - 30x -1 has no rational roots without using the rational root test? (since it is very long and tedious and no calculators are allowed) I was trying to prove this by contradiction. Suppose x=m/n is a rational root in lowest terms. But I am stuck at arriving at a contradiction...how can I possibly do so? Any insights? Thanks for any help!