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, so now, and therefore: , and finally, we have .