Question 1013304
12x^3 +53x^2 -34x+5=0 
They are +/- 5,5/2,5/3,5/4,5/6,5/12,1,1/2,1/3,1/4,1/6, 1/12
Factors of 5 over factors of 12
12==53==-34+5
Because 53 is prime, try an integer, and -5 works
12
===-60
====-7
=======35
========1
===========-5
===========0
(x+5)(12x^2-7x+1); the latter factors into (4x-1)(3x-1)
the roots are (-5,+(1/3),+(1/4))
{{{graph(300,200,-6,2,-50,50,12x^3 +53x^2 -34x+5)}}}