x^4 + 5x^3 + 7x^2 - 3x - 10 = 0
If we add the coefficients and constant term and get 0 then 1 is a root....so....
1 + 5 + 7 - 3 - 10 = 13 - 13 = 0
So 1 is a root
So.....we need to check wheter 2 is a root...if not....then -2 must be the other rational root
So
(2)^4 + 5(4)^3 + 7(2)^2 - 3(2) - 10 > 0
So -2 is the other rational root
So -2, 1 are the rational roots