Final answer:
The cubic polynomial corresponding to the given sum and product of zeros is f(x)= x³ - 3x² - x + 3.
Step-by-step explanation:
To find the cubic polynomial from given roots, we can use the sums and products of the roots. It is given that the sum of the roots (α, β, γ) is given as α+β+γ = 3, the sum of the product of the roots taken two at a time (αβ, βγ, γα) is given as αβ +βγ +γα = -1, and that the product of the roots (α β γ) is αβγ = -3.
We use the standard form of a cubicpolynomial which is given by f(x)= x³ - (sum of roots)x² + (sum of product of roots taken two at a time)x - (product of the roots). Substituting the given values, we get the cubic polynomial:
f(x)= x³ - 3x² - x + 3
Learn more about cubicpolynomial