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# Help with Rational Roots Polynomials

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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?

±12

±13

±118

±3

Nov 1, 2018

#1
+102948
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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

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

Nov 1, 2018
#2
+381
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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
#3
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Are you home-schooled ???

If so.......this stuff is very difficult to learn on your own....hang in there  !!!!

CPhill  Nov 1, 2018