Problem
ALG-B1-M04-P004 Three Values
#4
★★☆☆☆ Level 2 of 5
Quadratic polynomials \(P\) and \(Q\) have equal values at \(x=-1,0,2\). Prove that \(P=Q\).
Consider \(P-Q\).
The polynomial \(R=P-Q\) has degree at most \(2\) and three distinct roots: \(-1,0,2\). Hence \(R\equiv0\), so \(P=Q\).
A key principle for the whole module.