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Polynomialshard
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Let P(z)=z3+9z2+27z+27P(z) = z^3 + 9z^2 + 27z + 27P(z)=z3+9z2+27z+27. If the roots of P(z)=0P(z) = 0P(z)=0 are ω1,ω2,ω3\omega_1, \omega_2, \omega_3ω1​,ω2​,ω3​, what is the value of ω12+ω22+ω32\omega_1^2 + \omega_2^2 + \omega_3^2ω12​+ω22​+ω32​?