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Math Help - third-degree polynomial with real coefficients

  1. #1
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    third-degree polynomial with real coefficients

    find a third-degree polynomial with real coefficients and with zeros -3 +i and -4 are zeros
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  2. #2
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    Re: third-degree polynomial with real coefficients

    Hello, yuppie!

    Find a third-degree polynomial with real coefficients and with zeros -3 +i and -4.

    Complex roots always appear in conjugate pairs.
    Hence, if -3+i is a root, then -3-i is also a root.

    The cubic is: . \big(x - [-4]\big)\,\big(x - [-3+i]\big)\,\big(x - [-3-i]\big)

    . . . . . . . . =\;(x+4)(x+3-i)(x+3+i)

    . . . . . . . . =\;(x+4)(x^2+6x+10)

    . . . . . . . . =\;x^3 + 10x^2 + 34x + 40
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