The graph of a quadratic polynomial p(x)=ax2+bx+c has the following features:
• The parabola opens downwards.
• The vertex lies on the positive y–axis.
• It intersects the x–axis at two distinct points, both of which have positive x–coordinates.
Without performing any explicit numerical calculation, answer the questions that follow, giving brief reasons for each answer.
(i) State the sign (positive, negative or zero) of the coefficient a.
(ii) State the sign of the constant term c.
(iii) Comment on the signs of the two zeros of p(x).
(iv) State whether the discriminant b2−4ac is positive, zero or negative.