Upper limit for the zeros of 2x^4-7x^3+4x^2+7x-6=0

since the coefficients add to 0 we know that one root is x = 1, do synthetic division;

(x - 1) (2 x^3 - 5 x² - x + 6) ... now it is easy to see that x = - 1 is a root;

again synthetic division yields (x - 1) (x + 1) [ 2 x² - 7 x + 6 ]] ... so

the smallest upper bound is x = 2 { poly = 0 at x = 2 } ...

thus both 4 & 5 are upper bounds

and since you only ask to find an upper bound then x = 1000 is certainly an answer;

finally if you write the polynomial as " x [ x (x {2x - 7 } + 4) + 7 ] - 6 "

you can see that x = 3 is an upper bound