A polynomial with integer coefficients is of the form \(7x^4 + a_3 x^3 + a_2 x^2 + a_1 x - 14 = 0\). Find the number of different possible rational roots of this polynomial.

Guest May 21, 2019

#1**0 **

I might be simplifying this too much but there can only be a maximum of 4 becasue 4 is the degree.

Maybe there is less than 4

Melody May 21, 2019

#2**+1 **

I don't think you umderstood the question. The guest is not asking for the maximal amount of rational roots the polynomial can have.

Guest May 21, 2019

#4**+2 **

any rational roots are a factor of the constant term divided by a factor of the coefficient of the highest degree term.

here the constant term is -14 with factors +/- 1, +/- 2, +/- 7 +/- 14

and the leading coefficient is 7 with factors +/- 1, +/- 7

thus we have possible rational roots

+/- 1/7

+/- 2/7

+/- 1

+/- 2

+/- 7

+/- 14

a total of 12 possible rational roots

Rom
May 21, 2019