What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i? f (x) = x2 - 2x + 2 f (x) = x3 - x2 + 4x - 2 f (x) = x3 - 3x2 + 4x - 2 f (x) = x2 - x + 2

If a+bi is a root in a polynomial with real coefients, then a-bi is also a root

since 1+i is a root, 1-i is alos a root

a function that has the roots r1, r2 can be factored into form

f (x) = a (x-r1) (x-r2)

a is leading coefient

a=1 in this equation

r1=1+i

r2=1-i

r3=1

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

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

do math stuff

remember that i²=-1

f (x) = x³-3x²+4x-2