Answer:
p(x) = x³ - 7x² + 25x - 39
Step-by-step explanation:
complex roots occur as conjugate pairs, thus
2 + 3i is a root then 2 - 3i is also a root
given x = 3, x = 2 +3i, x = 2 - 3i are roots, then
(x - 3), (x - (2 + 3i))(x - (2 - 3i)) are the factors and
p(x) = a(x - 3)(x - 2 - 3i)(x - 2 + 3i) ← a is a multiplier
let a = 1
p(x) = (x - 3)((x - 2)² - 9i²)
= (x - 3)(x² - 4x + 4 + 9) → [ i² = - 1 ]
= (x - 3)(x² - 4x + 13)
= x³ - 4x² + 13x - 3x² + 12x - 39
= x³ - 7x² + 25x - 39
