How do you use the rational root theorem to find the roots of # f(x)=x^5-3x^2-4#?

1 Answer
Aug 21, 2015

Answer:

(as far as I can tell) #f(x)=x^5-3x^2-4# does not have any rational roots (and therefore the Rational Root Theorem is of no use in determining the roots)

Explanation:

According to the Rational Root Theorem:
any rational roots of #color(red)(1)x^5-3x^2-color(blue)(4)#
must be of the form:
#color(white)("XXXX")("integer factor of "color(blue)(4))/("integer factor of "color(red)(1))#

The only possible rational roots are therefore:
#color(white)("XXXX") +-1, +-2, +-4#

#f(+1) = -6#
#f(-1) = -8#
#f(+2)=16#
#f(-2) =-48#
#f(+4)=972#
#f(-4)=-1076#
Since none of these give a value for #f(x)# which is equal to #0#
all possible rational roots provided by the Rational Root Theorem are extraneous.