SOLUTION: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. −2 , −3+i thanks in advance.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. −2 , −3+i thanks in advance.       Log On


   

Question 939766: Find a polynomial
f(x) of degree 3 with real coefficients and the following zeros.
−2 , −3+i
thanks in advance.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find a polynomial
f(x) of degree 3 with real coefficients and the following zeros.
−2 , −3+i
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If the coefficients are Real and -3+i is a zero, then -3-i
is also a zero.
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Ans: f(x) = (x+2)(x-(-3+i))(x-(-3-i))
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= (x+2)((x+3)-i)((x+3)+i)
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= (x+2)[(x+3)^2+1]
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= (x+2)(x^2 + 6x + 10)
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= x^3 + 8x^2 +22x + 20
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Cheers,
Stan H.
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