Let V be vector space of Polynomial of degree 2 over R.fix t1<t2<t3 in R.Define fi belonging to V* (dual of v) by fi(p(x))=p(ti) for all p(x) in V,i=1,2,3.
Consider p1(x),p2(x),p3(x) in V by requiring that fi(pj) = 1 ,if i=j and 0 ,if i not equals j, i.e; p1(x) = (x-t2)(x-t3)/(t1-t2)(t1-t3) ,
p2(x)=(x-t1)(x-t3)/(t2-t1)(t2-t3) ,
p3(x)=(x-t1)(x-t2)/(t3-t1)(t3-t2) .
Now given c1,c2,c3 in R ,prove that there exist unique p(x) in V such that p(ti)=ci, for all i=1,2,3..
thank you in advance