# Using the rational root theorem, what are the possible rational roots of #x^3-34x+12=0# ?

##### 1 Answer

Oct 6, 2016

According to the theorem, the possible rational roots are:

#+-1# ,#+-2# ,#+-3# ,#+-4# ,#+-6# ,#+-12#

#### Explanation:

By the rational root theorem, any *rational* zeros of

That means that the only possible *rational* zeros are:

#+-1# ,#+-2# ,#+-3# ,#+-4# ,#+-6# ,#+-12#

Trying each in turn, we eventually find that:

#f(color(blue)(-6)) = (color(blue)(-6))^3-34(color(blue)(-6))+12#

#color(white)(f(color(white)(-6))) = -216+204+12#

#color(white)(f(color(white)(-6))) = 0#

So

The other two roots are Real but irrational.