Consider the polynomial g(x)=x4+px3+qx2+rx−20.
(i) It is given that x=2 is a zero of g(x). Write the corresponding condition on p,q, and r.
(ii) It is also given that x=−4 is a zero of g(x). Write the second condition on p,q, and r.
(iii) When g(x) is divided by (x−1), the remainder is 10. Write the third condition on p,q, and r.
(iv) Solve the simultaneous equations obtained in parts (i)–(iii) to find the values of p,q, and r.