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anonymous

  • one year ago

Form a third-degree polynomial function with real coefficients such that 7 + i and -4 are zeros. f(x)=

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  1. campbell_st
    • one year ago
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    well one of the factors is a quadratic with complex roots so start with that the roots is \[x = 7 \pm i\] subtract 7 from both sides of the equation. \[x - 7 = \pm i\] square both sides of the equation \[(x -7)^2 = i^2\] you need to remember i^2 = -1 so then its \[(x -7)^2 = -1~~~or~~~~(x -7)^2 + 1 = 0\] so you need to simplify \[(x -7)^2 + 1 \] to get the quadratic factor. the linear factor is when x = -4 or x + 4 is the linear factor... then the polynomial is \[P(x) = (x +4)[(x - 7)^2 + 1] \] simplify the equation

  2. anonymous
    • one year ago
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    Ahhh, I see! Thank you. :-)

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