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A polynomial with integer coefficients is of the form 

 

\(9x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 15 = 0\)


Find the number of different possible rational roots of this polynomial.

 

Thank you :D

 Feb 10, 2020
 #1
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The number 15 has four factors (1, 3, 5, 15), and the number 9 has three factors (1, 3, 9), so the total number of possible rational roots is 4*3 = 12.

 Feb 10, 2020
 #2
avatar+109561 
+2

The  possible  rational  roots   is given by  

 

± All  the possible factors of  15   divided by  All the possible factors of  9

 

Factors  of  15 =   1, 3, 5, 15

 

Factors  of  9  =  1, 3 , 9

 

So...all  the possible rational roots  =    ± (  1 , 1/3 , 1/9 , 3,  5 , 5/3 , 5/9 , 15  )

 

So.....16  possible rational roots

 

Thanks to DragonLord for catching my earlier error   !!!!

 

 

cool cool cool

 Feb 11, 2020
edited by CPhill  Feb 11, 2020
 #3
avatar+278 
+2

I see, thank you for your help, Cphill and Guest!!! <3

 Feb 11, 2020
 #4
avatar+278 
+2

CPhill, only a slight mistake. 15/9=5/3, other than that. Good!!! So, I'm pretty sure it would be 16. <3

 Feb 11, 2020
 #5
avatar+109561 
+2

Yep....thanks, DragonLord....I realized my mistake later on.....16 is correct  !!!

 

cool cool cool

CPhill  Feb 11, 2020
 #6
avatar+278 
+1

Np!!! Thank you for the explanation of how the rational root thereom is used :D. Everyone makes mistakes. I do as well. I just keep practicing. <3 laugh

 Feb 11, 2020

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