Question

What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i?

Answer 1

Answer:

f(x) = x3 – 3x2 + 4x – 2

Step-by-step explanation:

Answer 2

x³ - 3x² + 4x - 2

complex roots occur in conjugate pairs

1 + i is a root then so is 1 - i

the factors of the polynomial are therefore

f(x) = (x - 1 )(x - (1 + i))(x - (1 - i))

     = (x - 1 )(x² - 2x + 2 ) ( expand factors and simplify )

     = x³ - 3x² + 4x - 2