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# Algebra 2 polynomial

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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
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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   !!!!

Feb 11, 2020
edited by CPhill  Feb 11, 2020
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I see, thank you for your help, Cphill and Guest!!! <3

Feb 11, 2020
#4
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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
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Yep....thanks, DragonLord....I realized my mistake later on.....16 is correct  !!!

CPhill  Feb 11, 2020
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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

Feb 11, 2020