Question 180460
 {{{ graph( 300, 300, -5, 10, -10, 10, x^4-7x^3+18x-126) }}} 
Looks like x=7 is a root. 
{{{7^4-7(7)^3+18(7)-126=0}}}
{{{126-126=0}}}
You can iterate to find another root is between x=-2 and x=-3 at about x=-2.62074.
We can do a long division to find the exact value.
{{{(x^4-7x^3+18x-126)/(x-7)=x^3+18}}}
{{{x^3=-18}}}
{{{x=-18^(1/3)}}}
or approximately,
{{{x=-2.62074}}}
Is that what you were looking for??