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Abstract algebra

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.

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

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