Answer to Question #206645 in Abstract Algebra for Yogesh yadav

Question

 Showthatthe Polynomial x7-1oxs+15x+5 is not Solvable by ..

Answer 1

Show that the polynomial of x⁷−10x⁵+15x+5 is not solvable by radicals.

Using Descartes Law of Signs:

2 sign changes means 2 possible positive real roots

for f(-x)= -x⁷+10x⁵-5x+5

3 sign changes means 3 or 1 possible positive real roots

The polynomial can have maximum 5 real roots. So, at least 2 roots are complex.