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A polynomial with integer coefficients is of the form
\[2x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 45 = 0.\]
Find the number of different possible rational roots of this polynomial.

 Jun 29, 2022
 #1
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The possible rational roots come from :

 

All the factors of 45 =    ± [ 1, 3 , 5 , 9 , 15,  45 ] 

 

Divided by

 

All the  factors of  2 = ± [ 1, 2]

 

So we have

 

± [  1/2 , 3/2 5/2 , 9/2 , 15/2, 45/2 , 1, 3, 5 , 9, 15 ,45  ]

 

 

cool cool cool

 Jun 29, 2022

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