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we can take the derivative of it and try to make it equal 1

f(x)= 4x^7+7x^3+9x-357
f'(x)= 28x^6+21x^2+9 = 1
28x^6 +21x^2 +8 = 0 has the same effect

we can use synthetic division and trial and error to try to come to the roots...

then its just a matter of digging in and getting dirty :)

\[x^{2n} \geq 0\ \forall{ x \in \mathbb{R}; n \in \mathbb{Z}}.\]
Therefore it is > 0 ...

Sorry, the LaTeX engine on this thing is pellet so those conditions may be a little odd looking

looks greek to me :)

x^{even} >= 0 for all x

that "A" means all x elements of R right?

So it + 9 > 1 for all x

"for all" yes

if the graph of the derivative doesnt hit the x axis, then right, there are no real root...

Yes, listen to amistre

ok, well thanks to both of you

youre welcome :)