Question

Find a polynomial with the sum, sum of the product of its zeros taken two at a time, and product its zeros as 3, -1 and -3 respectively.

Answer 1

Given α + β + γ = 3,αβ + βγ + γα = −1 and αβγ = −3

So, polynomial f(x) = k {x³ - x² (α + β + γ) + x(αβ + βγ + γα) − αβγ }

f(x) = k {x³ - 3x² - x + 3}, where k is any non-zero real number.