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information is given about a polynomial f(x) whose coeffiecients are real numbers. Find the remaining zeros of f.

degree4, zeros i, 9+i

**I am just not getting these coefficients. I know that there has to be an easier way to learn this. Please help!!

  • calculus - ,

    They want to know the:

    remaining zeros of f

  • calculus - ,

    complex roots come in pairs, so the others must be -i and 9-i.

    Algebra I, I believe.

  • calculus - ,

    The reason they specify real coefficeints is so that you know the complex roots come in conjugate pairs. Otherwise, it is not true, since

    (x-3)(x+i) = x^2 - 3x + ix - 3i
    = x^2 + (-3+i)x - 3i

    which is a perfectly useful quadratic, but its coefficients are not real, so the roots do not have to come in conjugate pairs.

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