Question 668777: Find the complex zeros of the polynomial function. Write f in factored form
f(x)=x^3-6x^2+13x-20
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! Consider the coefficient of the highest degree, call it Q. Also consider the coefficient of the lowest degree (the constant) call it P. Find all factors of P and find all factors of Q , and take P/Q for each. Since Q is 1, this won't matter.
We get that the factors are {1,2,4,5,10,20}, plus or minus of course.
We are doing this because we want to find a 0 of the equation. So plug these different values until you get 0. It just so happens x =4.
Now do synthetic or long division:
(x^3-6x^2+13x-20)/(x-4) = x^2-2x +5
To finish this up, do the quadratic formula on x^2-2x+5 to obtain roots:
1-2i, 1+2i
Which means in factored form we have (x-4)(x-(1-2i))(x-(1+2i))
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