SILK-ROAD 2007 Problem 4

The set of polynomials $f_1, f_2, \ldots, f_n$ with real coefficients is called special, if for any different $i,j,k \in \{ 1,2, \ldots, n\}$ polynomial $\dfrac{2}{3}f_i + f_j + f_k$ has no real roots, but for any different $p,q,r,s \in \{ 1,2, \ldots, n\}$ of a polynomial $f_p + f_q + f_r + f_s$ 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?