Which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 - i) with multiplicity 1?

f (x) = (x + 7) (x - i) (x + 5) (x + i)

f (x) = (x - 7) (x - i) (x - 5) (x + i)

f (x) = (x - (7 - i)) (x - (5 + i)) (x - (7 + i)) (x - (5 - i))

f (x) = (x + (7 - i)) (x + (5 + i)) (x + (7 + i)) (x + (5 - i))

All of them have leading coefient of 1

roots of r1 and r2 have factors of

(x-r1) and (x-r2)

multiplicity 1 means that each factor doesn't repeat, it only appears once

so

roots (7+i) and (5-i)

f (x) = (x - (7+i)) (x - (5-i)) should be the answer

1st one is wrong, doesn't have roots

2nd is wrong, doesn't have roots

3rd has extra roots

4th is wrong

3rd one is right

f (x) = (x - (7 - i)) (x - (5 + i)) (x - (7 + i)) (x - (5 - i))