Question

if p(z)=z^3-az^2+bz-4 find the values of (a) and (b) if
p(2)=0

Answer 1

hope this helps

p(z)=z^3+az^2+bz+c
p(-2)=-8+4a-2b+c=0=>
4a-2b+c=8--------------(1)
If z is a root, then z divides p(z)
=>the remainder
(9+5a-3b+c)+(-12a+2b+46)i=0
=>5a-3b+c=-9----------(2)
.-12a+2b=-46
=>6a-b=23-------------(3)
Solving the system of (1),(2) & (3)
for a,b,c get
a=8
b=25
c=26

Answer 2

did you work that out ?

Answer 3

yes