SOLUTION: is it true that all real polynomials of odd degree has at least one real root? if it's true, what's the proof? if it's false, can you give a counter example?

Question 154464: is it true that all real polynomials of odd degree has at least one real root? if it's true, what's the proof? if it's false, can you give a counter example?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
That would be true.
Take for example y = x^3
When x is very negative y is verty negative.
But when x is very positive y is very positive.
If the function is continuous the y values must
have passed through zero; that means the yvalues
must have intersected the x-axis where y is zero.
And that intersection would be a Real Number zero
for the function.
I said this about a cubic equation; the same would
be true of any odd-powered function.
Cheers,
Stan H.
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