The sum of the zeros of a quadratic polynomial is −7 and their product is 12.
a. (i) Construct the quadratic polynomial with leading coefficient 1 that satisfies the above conditions.
b. (ii) Factorise your polynomial completely over the set of integers to verify your answer.
c. (iii) Sketch a rough graph of the polynomial, clearly marking the x-intercepts and the y-intercept.