If a and b are odd integers then find the number of integral roots of $(x^{10} +ax^9 +b=0)$

Question

If a and b are odd integers then find the number of integral roots of $(x^{10} +ax^9 +b=0)$

I've no idea how to solve this question. Any help would be appreciated. :|

See the Parity Root test. – Bill Dubuque Feb 07 '15 at 15:23 — Bill Dubuque, Feb 07 '15 at 15:23

score 2 · Accepted Answer · answered Feb 07 '15 at 13:23

2

You should consider the equation modulo $2$.

answered Feb 07 '15 at 13:23

MooS

I've not yet studied Modular arithmetic. Any other method pls? :) – Harshal Gajjar Feb 07 '15 at 13:25
Or maybe you could just elaborate a bit. :) – Harshal Gajjar Feb 07 '15 at 13:26
You dont need modular arithmetic for that. Just check the parity of $x^{10}+ax^9+b$ if $a,b$ are odd. For example, consider the two cases, $x$ even or $x$ odd. – MooS Feb 07 '15 at 13:27
1

He means consider both cases when $x$ is odd and even, and see if there can be solution in either case. – velut luna Feb 07 '15 at 13:27
He meant that you should consider what happens if x is odd, and what happens if x is even. – Lucian Feb 07 '15 at 13:28

score 1 · Answer 2 · answered Jul 27 '16 at 13:49

1

O. Eqn with odd integers; where D (∆) = not a perfect sq. Hence no intergral roots

answered Jul 27 '16 at 13:49

Rohan

I don't think that you have added much extra information to an old question. – Mc Cheng Jul 27 '16 at 14:01
@McCheng: On the contrary, this is a very good answer, unfortunately somewhat terse. – Alex M. Jul 27 '16 at 14:17

2 Answers2