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college alg

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form a polynomialf(x) with real coefficients, having the given degree and zeros

degree 5; zeros -5;-i; -5+i

  • college alg - ,

    If x = -i and x = -5 +i are roots, so must be x = i and x = -5 -i.
    A(x+5)(x-i)(x+i)(x+5+i)(x+5-i)= 0
    is a polynomial with those roots, where A is any constant.
    Let's set A = 1.

    That can be rewritten
    (x+5)(x^2 +1)(x^2 +10x +25 +1)= 0
    or
    (x^3 +5x^2 +x +5)(x^2 +10x +26) = 0

    Multiply that out for the full fifth order polynomial.

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