Question

Find all solutions of
\[x^{13}+7x^3-8=0\]

Answer 1

x=1 is a clear solution

Answer 2

how many solutions are there?

Answer 3

real solutions?

Answer 4

yes real

Answer 5

that's better.

Answer 6

\[x^{13}+7x^3-8\] is an increasing function

Answer 7

yes so we have just 1 real solution x=1

Answer 8

correct

Answer 9

\[p(x)=x^{13}-7x^3-8\]
only once sign changes so there is a positive root or no positive root
\[p(-x)=-x^{13}-7x^3-8\]
there is no sign changes so it has no negative root

we know that x=1 is a root and it is positive so all the rest roots are complex..