Let p(x)=kx2+(k−3)x+3, where k is a real constant.
a. (i) If x=1 is a zero of p(x), find the value of k.
b. (ii) Using the value of k obtained in part (i), find the remainder when p(x) is divided by (x+2).
c. (iii) For the same value of k, verify whether x=−2 is a zero of p(x).