Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

f(x) = 3x^3 + 39x^2 + 39x + 27

Question

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

f(x) = 3x^3 + 39x^2 + 39x + 27

hartnn · Answer

do u know rational zero theorem ??

anonymous · Answer

not really, ive been trying to figure this out... but my textbook isnt very clear

hartnn · Answer

then this reference might help, see solved example: http://en.wikipedia.org/wiki/Rational_root_theorem

hartnn · Answer

if u still don't understand, i'll explain.

anonymous · Answer

yeah.. that would be helpful

hartnn · Answer

ok 
list the factors of 27
and list the factors of 3

anonymous · Answer

1,3,9,27
and 1, 3

hartnn · Answer

yup, now comparing your equation with ax^2+bx+cx+d u get d=27,a=3 right
According to that theorem , the possible roots are given by all possible ratios in 
$\huge \frac{d}{a}=\frac{27}{3}=\frac{1,3,9,27}{1,3}$
so what all possibilities u have??

anonymous · Answer

you have... +/-....

1, 3/1, 9/1, 27/1, 1/3, 9/3, 27/3
i think

hartnn · Answer

yup, there is $\huge \pm$ sorry , i forgot that....so all those possibilities with negative sign also..... ok ?

anonymous · Answer

mmk, thank you so much! it makes way more sense now

hartnn · Answer

just note that u wrote 3/1 twice .... 3/1 and 9/3 ....

hartnn · Answer

and 9/1 twice .... 9/1 and 27/3 ....