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.
+118609
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
I don't think you umderstood the question. The guest is not asking for the maximal amount of rational roots the polynomial can have.
+6248 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
