Hello, OntarioStud!

How would you show that every polynomial of fifth degree has at least one real root?

Graphically, maybe?

Given: .

For positive and*

Since the polynomial function is continuous, itmustcross the x-axis somewhere.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

*.Of course, the argument hold for negative as well.