Verify x^(2n+1)+ax+b don't have 2 roots that a0 and n is integer.

Question

Verify x^(2n+1)+ax+b don't have 2 roots that a>0 and n is integer.

anonymous · Answer

Does any one can solve this :(

asnaseer · Answer

it doesn't have 2 roots - it has 2n+1 roots because its a polynomial of degree 2n+1

anonymous · Answer

my english is not good, i wish you can understand my explain.
you can consider the slope of every point on it, which is the derivation of this equation.
that is (2n+1)x^(2n)+a
which is always a positive value when a>0 and n is integer.
so the graph could be |dw:1339247524817:dw|
the line never goes down so it can not have more than 1answer.

anonymous · Answer

if you are still puzzle, say where.

asnaseer · Answer

do you mean it doesn't have 2 "real" roots?

asnaseer · Answer

and is the equation actually this?$$x^{2n+1}+ax+b=0$$

anonymous · Answer

yes

asnaseer · Answer

ok, so if you mean for this equation:$$x^{2n+1}+ax+b=0$$prove that there cannot be two or more "real" roots, then @AndrewNJ has explained it for you above.
He has shown that the slope is always positive everywhere on the curve which implies it cannot cross the x-axis more than once.

anonymous · Answer

Thank you @AndrewNJ and @asnaseer for help me sovle this :)

asnaseer · Answer

yw :)

anonymous · Answer

:)