Question

Hello, I need some help with Part 2 question 6! Please show work as the instructions asked! If you want me to include other completed work from the assignment for extra information, please let me know. Thank you.

Answer 1

Problem N 6

we have the roots

3 and (4+i)

By the conjugate complex theorem

If (4+i) is a root

then

(4-i) is a root too

so

we have at least

Zeros

x=3

x=4+i

x=4-i

The polynomial function is given by

(x-3)(x-(4+i))(x-(4-i))

Multiply first

(x-(4+i))(x-(4-i))

x^2+(4+i)(4-i)-x(4-i)-x(4+i)

x^2+16-i^2-4x+xi-4x-xi

x^2+16-(-1)-8x

x^2-8x+17

so

(x-3)(x-(4+i))(x-(4-i))=(x-3)(x^2-8x+17)

Apply distributive property again

x^3-8x^2+17x-3x^2+24x-51

x^3-11x^2+41x-51 ----> Polynomial function

therefore

The code is A