If a, b, c are non-zero real numbers such that a+b+c=0, then what are the roots of the equation ax^{2}+bx+c=0?

Explanation

Since a+b+c=0, substituting x=1 into the equation ax^2+bx+c=0 satisfies it, making 1 one of the roots. The product of the roots is given by \frac{c}{a}. Therefore, the other root must be \frac{c}{a}.

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