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.
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 ]
