Dear student,
Let α = 1, β = -2 and γ = 3
α + β + γ = 1 - 2 + 3 =2
αβ + βγ +γα = -2 - 6 + 3 = -5
αβγ = -6
Cubic polynomial is
x3 - (α + β + γ)x2 + (αβ + βγ +γα)x - αβγ.
= x3 - 2x2 + 5x + 6
For the remaining parts, kindly post in a separate thread to get rapid assistance from our experts. Regards!