Consider the two quadratic polynomials:
p(x)=2x2−5x+3,q(x)=4x2+6x−1.
(i) Compute the sum and the product of the zeros of p(x).
(ii) Compute the sum and the product of the zeros of q(x).
(iii) Using your answers, determine whether the following statements are true or false. Give reasons for each.
(a) The sum of the zeros of p(x) is greater than the sum of the zeros of q(x).
(b) The product of the zeros of q(x) is negative.
(iv) Without solving either quadratic equation, predict the number of real zeros (two distinct, one repeated, or none) each polynomial possesses. Justify your answer solely on the values obtained in parts (i) and (ii).