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A polynomial with integer coefficients is of the form
\[21x^4 + a_3 x^3 + a_2 x^2 + a_1 x - 28 = 0.\]
If $r$ is a rational root of this polynomial, then find the number of different possible values of $r.$

 Oct 11, 2023
 #1
avatar+128731 
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Rational Roots Theorem

 

Possible factors of 28  =   ±1, ±2 , ±4, ±7, ±14, ±28

 

Possible factors of 21  = ±1, ±3, ±7, ±21

 

Possible rational roots  =

 

All possible factors of 28  / All possible factors of  21   =

 

±1, ±2, ±4, ±7, ±14, ±28, ±1/3 , ±2/3, ±4/3 , ± 4/3, ±7/3, ±14/3, ±28/3, ± 1/7, ±2/7,±4/7, ±1/21, ±2/21, ±4/21,

 

cool cool cool

 Oct 11, 2023

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