Saturday, June 22, 2013

Find all other zeros of P(x)=x^3 -x^2 +8x +10, given that 1-3i is a zero.


x%5B1%5D=1-3i 
then
x%5B2%5D=1%2B3i 

%0D%0A%28x-1-3i%29%28x-1%2B3i%29=x%5E2-x-3ix-x%2B1%2B3i%2B3ix-3i%2B9%0D%0A 
so one factor must be 
%0D%0Ax%5E2-2x%2B10%0D%0A 
after long division... 
P%28x%29%2F%28x%5E2-2x%2B10%29=x%2B1 

zeros: 

{1-3i, 1+3i, -1}}}
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