The zeros of a quadratic polynomial are reciprocals of each other and their sum is −37.
(i) Find the two zeros.
(ii) Construct a quadratic polynomial whose constant term is 9 and which possesses these zeros.
(iii) Prove that for every quadratic polynomial having the zeros obtained in part (i), the coefficient of x equals −(sum of zeros) times the leading coefficient. Verify this statement for the polynomial you formed in part (ii).