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    Consider the cubic polynomial:
    See attached file for full problem description.
    Prove that if all 3 zeros are real, then all 3 coefficients are real.

    Consider the cubic polynomial:
    P(z) = z3 + a1z2 + a2z + a3
    Prove that if all 3 zeros are real, then all 3 coefficients are real.

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    https://brainmass.com/math/basic-algebra/abstract-algebra-polynomial-proof-64527

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    Consider the cubic polynomial:
    P(z) = z3 + a1z2 + a2z + a3
    Prove that if all 3 zeros are real, then all 3 coefficients are real.

    Proof
    Let r1 ,r2 ,r3 are three real zeros then
    P(z) = (z - r1) (z - r2) (z - r3) = 0
    comparing the coefficients
    ...

    Solution Summary

    If all three zeros are real, then all 3 coefficients are real.

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