Answer to Question #215687 in Abstract Algebra for Preeti

Question

x^5-9x+3 is polynomial are not solvable by radicals over Q

Answer 1

Abel Rufini's theorem states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Also, since the polynomial as defined is not an nth cyclotimic polynomial, we can safely conclude by these two assertions (stated above) that the polynomial is not solvable by radicals over Q