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

Where is the diagram?