Please help soon. Due tomorrow. Can anyone help me create a polynomial function with given zeros?

Question

The zeros are 2, 4 + i, 4 - i

The i is imaginary

I can get this far:

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

But I'm confused with the signs for the second and third sets of parenthesis. I'm not sure what signs are supposed to change or if I have them correct.

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Answer 1 · 2016-12-05T02:34:11

The zeros are #2#, and #4+i# and #4-i#

The factors are:
#(x-2)#, #" "# #(x-(4+i))#, #" "#, and #" "# #(x-(4-i))#

I would start by multiplying

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

# = x^2-4x+x i-4x - x i +(16-i^2)#

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

# = x^2-8x+17#

Note that I used the product of a sum and difference #(4+i)(4-i) = 16-i^2#. You can multiply htis out in more detail is you like.

Now multiply #(x-2)(x^2-8x+17)# to get

#x^3-8x^2+17x -2x^2+16x-34#

# = x^3-10x^2+33x-34#