SOLUTION: Write a 4th degree polynomial with integer coefficients that has no rational roots.

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Question 1173673: Write a 4th degree polynomial with integer coefficients that has no rational roots.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

x%5E4 + 1 = 0   (has no one real root, and in particular, has no one rational root).


x%5E4 = 4       (almost the same as  x%5E2 = 2,  has IRRATIONAL roots  x = +/- sqrt%282%29 ).



x%5E4 = 9       (almost the same as  x%5E2 = 3,  has IRRATIONAL roots  x = +/- sqrt%283%29 ).



And millions other examples.