math

Form a polynomial​ f(x) with real​ coefficients, with leading coefficient​ 1, having the given degree and zeros.
Degree: 4; zeros: -4+3i and 1; multiplicity of 2

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  1. if -4 + 3 i
    then -4 - 3 i is also a zero
    so
    (x + 4 - 3 i) (x + 4 + 3 i) ( x-1) (x-1) = y

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    Damon
  2. alternative way:

    f(x) = (x-1)^2 (a quadratic)
    complex roots always come in conjugate pairs, so -4 - 3i is another
    sum of the complex roots = -8
    product of the complex roots = (-4+3i)(-4 - 3i)
    = 16 - 9i^2 = 25
    so the quadratic part is x^2 + 8x + 25

    f(x) = (x^2 + 8x + 25)(x-1)^2

    of course you could also expand
    f(x) = (x - (-4+3i))(x - (-4-3i))(x-1)^2 to get the same thing
    this is how Damon did it

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    Reiny

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