Given that $a,b,c$ be three distinct real numbers then the number of distinct real roots of the equation $p(x)=(x-a)^3+(x-b)^3+(x-c)^3=0$ is
depends on $a,b,c$
what I did is $p'(x)=0$ which is two degree polynomial with three distinct root, so $p'(x)\equiv 0$ so $p(x)=k$ some constant, where I am wrong? Is the probelm wrong? Thank you for help.