Let
f(x)=4x2+kx+9andg(x)=x2+(k−2)x+(9−2k).
The product of the zeros of g(x) is required to be the same as that of f(x).
(i) Find the product of the zeros of f(x).
(ii) Write the condition that the product of the zeros of g(x) equals the value obtained in part (i) and hence determine the possible values of k.
(iii) For each admissible value of k, calculate the sum of the zeros of both polynomials and state whether these sums are equal, unequal, or opposite in sign.
(iv) Using your results, discuss how the choice of k affects the horizontal positions of the vertices of the two parabolas relative to the y–axis.