rmo 2010 Q

let P1(x)= ax^2-bx-c, P2(x)=bx^2-cx-a,P3(x)= cx^2-ax-b, be 3 quadritic polynomials where a,b,c are non zero real numbers suppose there exists a real number k such that P1(k) = P2(k)= P3(k). then prove that a=b=c.

please do it by the method of contradiction
[by assuming a≠b≠c and the follow up and contradict your statement.]
i know how to do it by the normal method.