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Question

1. Find all complex zeros of f(x)= x^4-8x^3+26x^2-32x+13, given that you know one of the zeros is 3+2i. Use the zeros to write the function in factored form. 

2. Identify any asymptote(s) and find the location of any hole(s) of the function. If they do not exist, write NONE and write any asymptotes as equations of lines. 

R(x)=2x^3+8x^2+6x/x^2+5x+6

Answer 1

Then 3-2i must be a zero.

The polynomial for these factors are (x-3)+2i and (x-3)-2i

Multiplying them: [(x-3) + 2i ][ (x-3) - 2i ]

= (x-3)^2 - (-4)

x^2 - 6x + 13

Next divides this polynomial into the original polynomial function. THe result shall be quadratic

x^2- 2x + 14

divides x^2 - 6x + 13 | x^4 - 8x^3 + 26x^2 - 32x + 13

x^4 - 6x^3

-----------------------------------------

-2x^3 + 26x^2

-2x^3 + 12x^2

------------------------

14x^2 - 32x

14x^2 - 84x

----------------

52x + 13

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