For a quadratic polynomial with leading coefficient
MATHEMATICS · Multi-part · AoPS · Mathematics · Quadratic Equations - Part 1 · Quadratic Equations - Part 1
Problem
For a quadratic polynomial with leading coefficient 3, the sum of its zeros is equal to twice their product. The product of the zeros is −32.
(i) Find the numerical value of the sum of the zeros.
(ii) Construct the quadratic polynomial in standard form.
(iii) Determine the discriminant of the polynomial and hence state the nature of its zeros.
(iv) Using the information obtained, sketch a rough graph of the polynomial, clearly indicating the points of intersection with the axes.