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Create a 3rd degree polynomial with real coefficients that has roots -1 and 4i. Write your answer in form ax^3 + bx^2 + cx+ .

  • Math -

    any complex roots come in conjugate pairs
    so if 4i is a root, so is -4i

    those two roots would come from (x^2 + 16 ) = 0
    so the polynomial would be

    a(x+1)(x^2 + 16)
    = a(x^3 + x^2 + 16x + 16)

    if we assume a = 1
    a possible polynomial would be

    x^3 + x^2 + 16x + 16

    (or any multiple of that)

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