2010 AIME II Problems/Problem 7
Let , where a, b, and c are real. There exists a complex number such that the three roots of are , , and , where . Find .
set , so , , .
Since , the imaginary part of a,b,c must be 0.
Start with a, since it's the easiest one to do:
and therefore: , ,
now, do the part where the imaginery part of c is 0, since it's the second easiest one to do: , the imaginery part is: , which is 0, and therefore x=4, since x=0 don't work
and therefore: , and finally, we have .