The set of polynomials f1,f2,…,fn with real coefficients is called special , if for any different i,j,k∈{1,2,…,n} polynomial 32fi+fj+fk has no real roots, but for any different p,q,r,s∈{1,2,…,n} of a polynomial fp+fq+fr+fs there is a real root.
a) Give an example of a special set of four polynomials whose sum is not a zero polynomial.
b) Is there a special set of five polynomials? algebrapolynomialReal Roots