If ${\mathrm{x}}_1, {\mathrm{x}}_2, {\mathrm{x}}_3$ are distinct roots of the equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$ then

Since quadratic equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$ has three distinct roots so it must be an identity.

So $\mathrm{a}=\mathrm{b}=\mathrm{c}=0.$