Question

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.

2+​i, 1

Answer 1

x³ - 5x² + 9x - 5

Explanation:

If one root is 2 + i, other has to be 2 - i.

So at least 3 roots, minimum degree is 3

(x - 2 - i)(x - 2 + i)(x - 1)

[(x - 2)² - (i)²](x - 1)

(x² - 4x + 4 + 1)(x - 1)

(x² - 4x + 5)(x - 1)

x³ - 4x² + 5x - x² + 4x - 5

x³ - 5x² + 9x - 5