Which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 – i) with multiplicity 1?
a. f(x) = (x + 7)(x – i)(x + 5)(x + i)
b. f(x) = (x – 7)(x – i)(x – 5)(x + i)
c. f(x) = (x – (7 – – (5 + – (7 + – (5 – i))
d. f(x) = (x + (7 – + (5 + + (7 + + (5 – i))

C.

Step-by-step explanation:

We want to find the equation of a polynomial the following properties;

i. Leading coefficient is 1

ii. roots (7 + i) and (5 – i) with multiplicity 1

Recall the complex conjugate properties of the roots of a polynomial.

According to this property, if

is a root of a polynomial, then the complex conjugate,  is also a root.

This means that:

(7 - i) and (5 + i) with multiplicity 1 are also roots of this polynomial.

The complete set of roots are:

Therefore the polynomial is:

The correct choice is C.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

b

step-by-step explanation:

u take $75 minus $60.the anwer/original($75)multiply by 100