Question 72344This question is from textbook
: for the polynominal, one zero is given. Find all the others:
f(x)= x^4 + 10x^3 + 27x^2 + 10x + 26; i
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! for the polynominal, one zero is given. Find all the others:
f(x)= x^4 + 10x^3 + 27x^2 + 10x + 26; i
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If "i" is a zero, then "-i" is also a zero.
Therefore (x-i)(x+i)=x^2+1 is a factor.
Dividing by x^2+1 the quotient is x^2+10x+26
The roots of this quadratic are:
x=[-10+-sqrt(100-4*26)]/2
x=[-10+-sqrt(-4)]/2
x=[-5+-i]
x=5+i or x=5-i or x=i or x=-i
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Cheers,
Stan H.
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