Question

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Answer 1

using formula

x^3-(alpha+beta+gamma)x^2+(alpha*beta+beta*gamma+gamma*alpha)- alpha*beta*gamma

now,

#alpha+beta+gamma=3

#alpha*beta+beta*gamma+gamma*alpha=-1

#alpha*beta*gamma=-1/3

using up the value

x^3-3x^2+(-1)x-(-1/3)

x^3-3x^2-x+1/3

lcm=3x^3-9x^2-3x+1/3

required polynomial is

3x^3-9x^2-3x+1