Consider the quadratic polynomial p(x)=ax2+bx+c with a=0.
(i) Explain why the sign of b influences whether the sum of the zeros is positive, negative or zero.
(ii) If c is negative, what can you conclude about the sign of the product of the zeros? Give a brief reasoning.
(iii) Give one example of a quadratic polynomial with integer coefficients whose sum of zeros is positive while the product of zeros is negative. Verify your claim for the polynomial you have chosen.