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.