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.
Please and thank you! 0^>
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 :
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. :)