The roots of a quadratic equation ax2+bx+c=0 are 1+i 5 and 1−i 5 . find possible values of a, b and c.

Step-by-step explanation:

If the roots are 1 + 5i and 1 - 5i, then you need the factors that result from those roots.  They are (x - 1 + 5i) and (x - 1 - 5i).  Now what you do with those is FOIL them out.  Doing that gives you the following:

(what a mess, huh?)

The good thing is that several of those terms cancel each other out.  +5ix cancels out the -5ix; -5i cancels out the 5i; and the 2 -x terms combine to -2x.  That leaves you with:

Obviously you're in the section in math that deals with complex (imaginary) numbers so you should know that i-squared is equal to -1.  Making that replacement:

a = 1, b = -2, c = 25