Let p(x)=3x2+kx+2 be a quadratic polynomial.
a. (i) Determine the value of k for which (x−2) is a factor of p(x).
b. (ii) For this value of k, factorise p(x) completely.
c. (iii) Using the factorised form, obtain the zeros of the polynomial and verify that their sum and product agree with the relationships between coefficients and zeros of a quadratic polynomial.