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A degree 4 polynomial with integer coefficients has zeros −1−2i and 1, with 1 a zero of multiplicity 2. If the coefficient of x^4 is 1, 
then the polynomial is

 Mar 12, 2019
edited by Guest  Mar 12, 2019

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 #1
avatar+8341 
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\(f(x) = (x - 1)^2 (x - (-1-2i))(x - r) \text{ for some } r \in \mathbb C\)

But the polynomial has integer coefficients, so \(r = \overline{-1-2i} = -1+2i\).

\(f(x) = (x^2 - 2x + 1) (x^2 + 2x + 5) \\f(x)= x^4+2x^2-8x+5\)

 Mar 12, 2019
 #1
avatar+8341 
+1
Best Answer

\(f(x) = (x - 1)^2 (x - (-1-2i))(x - r) \text{ for some } r \in \mathbb C\)

But the polynomial has integer coefficients, so \(r = \overline{-1-2i} = -1+2i\).

\(f(x) = (x^2 - 2x + 1) (x^2 + 2x + 5) \\f(x)= x^4+2x^2-8x+5\)

MaxWong Mar 12, 2019

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