# hw11 - (2 Find all constructible roots of the equation x...

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You do not need to turn in these problems. They are just practice problems on the material of the last lecture. (1) (a) Let f ( x ) = a n x n + ...a 1 x + a 0 be a polynopmial with integer coeﬃcients. Suppose x 0 = p q is a root of f ( x ) = 0 where p,q Z and ( p,q ) = 1. Show that p | a 0 and q | a n . (b) Show that the equation 3 x 5 - 2 x 3 - x 2 - 2 = 0 has no rational solutions.
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Unformatted text preview: (2) Find all constructible roots of the equation x 4-2 x 3-2 x 2 + 9 x-10 = 0 (3) Let 0 < θ < π/ 2 be the angle with cos θ = 2 7 . Show that θ is constructible but θ/ 3 is not. (4) Show that the equation x 9-4 x 3 + 1 = 0 has no constructible roots. 1...
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## This note was uploaded on 04/26/2011 for the course MATH 246 taught by Professor Applebaugh during the Spring '10 term at University of Toronto.

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