Answer:
Step-by-step explanation:
Given a polynomial with:
- The leading coefficient is - 3
- Roots are 4, 0, 5 - 2i
We know the complex roots should be paired with their conjugate.
So 5 + 2i is also a root.
The least polynomial is:
f(x) = - 3(x - 4)(x - 0)(x - 5 - 2i)(x - 5 + 2i) =
-3x(x - 4)(x² - 10x + 29) =
-3x(x³ - 14x² + 69x - 116) =
-3x⁴ + 42x³ - 207x² + 348x
