Find a polynomial function of least degree having only real coefficients, a leading of 1, and zeros of 2 and 2+i.

y = x³ - 6x² + 13x - 10

Step-by-step explanation:

Complex roots come in pairs, so if 2 + i is a root, then 2 - i is also a root.

y = (x - 2) (x - (2 + i)) (x - (2 - i))

y = (x - 2) (x - 2 - i) (x - 2 + i)

y = (x - 2) ((x - 2) ² - i²)

y = (x - 2) (x² - 4x + 5)

y = x (x² - 4x + 5) - 2 (x² - 4x + 5)

y = x³ - 4x² + 5x - 2x² + 8x - 10

y = x³ - 6x² + 13x - 10