Let α, β and γ are the zeroes of the required polynomial.
Then we have:
α + β + γ = 3 + 5 + (-2) = 6
αβ + βγ + γα = 3 × 5 + 5 × (-2) + (-2) × 3 = -1
and αβγ = 3 × 5 × -2 = -30
Now, p(x) = x3 – x2 (α + β + γ) + x (αβ + βγ + γα) – αβγ
= x3 – x2 × 6 + x × (-1) – (-30)
= x3 – 6x2 – x + 30
So,
the required polynomial is p(x) = x3 – 6x2 – x + 30.