c. since p(x) has two turning points, p'(x) must have two real solutions.
p'(x) = 3x^2 +c. to confirm you can use discriminant is > 0.
0^2-4(3)(c)>0.
so -12c>0, c<0
d. use sum of roots. a+ib + a-ib + k = 0.
2a +k=0
a=-k/2 but since k<0, that means a>0.