Final answer:
The equation of least degree with zeros at 8 and 2 + i, accounting for the conjugate pair, is x³ - 12x² + 37x - 40.
Step-by-step explanation:
To find the equation of least degree for a polynomial function given zeros of 8 and 2 + i, we first need to understand that complex roots come in conjugate pairs.
Hence, if 2 + i is a zero, its complex conjugate, 2 - i, is also a zero.
We can then form factors for each zero: (x - 8) for the zero at 8, and (x - (2 + i)), (x - (2 - i)) for the complex zeros.
The factors corresponding to the complex zeros multiply to a quadratic with real coefficients:
(x - 2 - i)(x - 2 + i) = x² - 4x + (2² + i²)
= x² - 4x + 5.
Combining this with the factor for the real zero, we have the polynomial:
(x - 8)(x² - 4x + 5).
To find the equation, we expand the factors to get: x³ - 4x² + 5x - 8x² + 32x - 40, which simplifies to x³ - 12x² + 37x - 40.
Therefore, the equation of least degree that satisfies the given zeros is x³ - 12x² + 37x - 40.