math- finding zeros

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Using the given zero, find all the zeroes and write a linear factorization of f(x)

1 + i is a zero of f(x)= x4-2x^3-x^2 + 6x -6
I did synthetic division and I got that it wasn't a zero?

  • math- finding zeros -

    This is a trick question.

    We know that complex roots always come in pairs. If 1+i is a root, so is 1-i, its conjugate.

    The given root and its conjugate multiplied together become a real factor, namely (x-1-i)(x-1+i)=x^2-2*x+2.
    Repeat your synthetic division using the combined real factor and you will have a quotient of x²-3.

  • math- finding zeros -

    oh yeah, I forgot about the conjugates! thanks!

    One more question, how do i divide x^4-2x^3-x^2+6x-6 by x^2-2x+2 using synthetic division?

  • math- finding zeros -

    It's a similar process as long division with numbers.

    Check out web resources such as:
    http://www.purplemath.com/modules/synthdiv2.htm
    or
    http://www.youtube.com/watch?v=bZoMz1Cy1T4

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