Question 427134: Determine graphically the number of real zeros and the number of imaginary zeros of the polynomial function f(x) = x^3 - 3x^2 + 3x - 9.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Determine graphically the number of real zeros and the number of imaginary zeros of the polynomial function f(x) = x^3 - 3x^2 + 3x - 9.
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f(x)=x^3-3x^2+3x-9
If you are allowed to use a graphing calculator, you will see that the function has only one real zero, x=3.
(see the graph below). After this, divide the function,x^3-3x^2+3x-9, by (x-3) by long division or synthetic division. You will then get a quotient,(x^2+3), which gives you two imaginary zeros.
ans:
one real zero=3
two imaginary zeros=+-sqrt(-3) or +-sqrt(3)i
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After reviewing my above solution, I realized the function could be factored:
x^3-3x^2+3x-9=x^2(x-3)+3(x-3)=(x-3)(x^2+3)
This would give you one real zero, 3 and two +-sqrt(-3), imaginary zeros, same as above.
This is the preferred method as you do not require a calculator for the solution.
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