Could someone help explain this to me?

Which values are possible rational roots of 9x3+14x2−x+18=0 according to the rational root theorem?

Select each correct answer.

±12

±13

±118

±3

*Please and thank you! 0^>*

PhoenixForever
Nov 1, 2018

#1**+2 **

In the form ax^n + bx^m +....... + c = 0

The* possible* rational roots [ rational meaning that we can express a number as a fraction] are all the possible factors of "c" over all the possible factors of "a"

So we have

9x^3 + 14x^2 - x + 18 = 0

So...all the possible factors of c = 18 are ±18, ±9, ±6, ±3, ±2, ±1

And all the possible factors of a = 9 are ±9, ±3, ±1

So....in your answer...all the possible rational roots are ±1/3 and ±3/1

Note that ±1/2 isn't possible because ±2 isn't a factor of 9

And ±1/ 18 isn't possibe because ±18 isn't a factor of 9

Note something, PhoenixForever......this does not mean that these are necessarily the roots of the equation....they are just * possible* roots...!!!

Here's a resource I always like, Purplemath....it explains this in more detail than I can :

https://www.purplemath.com/modules/rtnlroot.htm

CPhill
Nov 1, 2018

#2**+1 **

Thank you very much for explaining possible roots and for the extra resource as well! Sometimes the curriculum I am on doesn't teach new concepts very thoroughly. :)

PhoenixForever
Nov 1, 2018