what are roots of ax^2+bx+c=0 such that a+b+c=0
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Let roots be x and y
then x+y = b/a and xy = c/a
So b = ax+ay and c = axy
Now as given a+b+c = 0
a+ax+ay+axy = 0
a(1+x+y+xy) = 0
So now 1+x+y+xy = 0
then 1+x +y(1+x) = 0
=> (1+x)(1+y) = 0
So x = -1 and y = -1 .
then x+y = b/a and xy = c/a
So b = ax+ay and c = axy
Now as given a+b+c = 0
a+ax+ay+axy = 0
a(1+x+y+xy) = 0
So now 1+x+y+xy = 0
then 1+x +y(1+x) = 0
=> (1+x)(1+y) = 0
So x = -1 and y = -1 .
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