# show the poly has one and only one root.

• Apr 24th 2010, 07:41 PM
alice8675309
show the poly has one and only one root.
Show that the polynomial $x^4$+10x-12 has one and only one root in the interval (0,2). I don't understand how I would make aproof for this.
• Apr 24th 2010, 08:04 PM
Prove It
Quote:

Originally Posted by alice8675309
Show that the polynomial $x^4$+10x-12 has one and only one root in the interval (0,2). I don't understand how I would make aproof for this.

If a function has more than one root, then the function must turn at some point in between them. So to show that there is only one root, show that there are not any turning points.