Question 86736: I can't figure out even where to start with this question, could you walk me through it????
Find a polynomial with integer coefficients that has the given zeros. -4, -1+i, -1-i
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find a polynomial with integer coefficients that has the given zeros. -4, -1+i, -1-i
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If -4 is a zero, (x+4) is a factor.
If -1+i is a zero, (x-(-1+i))= ((x+1)-i) is a factor
If -1-i is a zero, (x-(-1-i))= ((x+1)+i) is a factor
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The polynomial you want is the product of these factors:
f(x)=(x+4)((x+1)^2-(i^2))
f(x)=(x+4)((x+1)^2+1)
f(x)=(x+4)(x^2+2x+2)
f(x)=x^3+6x^2+10x+8
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Cheers,
stan H.
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