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

DragonLord Feb 10, 2020

#1**0 **

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.

Guest Feb 10, 2020

#2**+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 !!!!

CPhill Feb 11, 2020

#4**+2 **

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

DragonLord Feb 11, 2020

#6**+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

DragonLord Feb 11, 2020