SOLUTION: If x+4-4i is a factor of the function f(x) = px^2 + qx + r, show that p,q and r are in geometric progression

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: If x+4-4i is a factor of the function f(x) = px^2 + qx + r, show that p,q and r are in geometric progression      Log On


   

Question 1045476: If x+4-4i is a factor of the function f(x) = px^2 + qx + r, show that p,q and r are in geometric progression
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Not sure if x is real or can be complex.

%28x%2B4-4i%29%28x%2B4%2B4i%29=px%5E2%2Bqx%2Br
%28%28x%2B4%29-4i%29%28%28x%2B4%29%2B4i%29=px%5E2%2Bqx%2Br
%28x%2B4%29%5E2-%2816%29%28-1%29
x%5E2%2B16x%2B16%2B16
x%5E2%2B16x%2B32=px%5E2%2Bqx%2Br

system%28p=1%2Cq=16%2Cr=32%29 but these are not in successive geometric progression.