document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #297049 by lwsshak3(11628)\"\" \"About 
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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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\n" ); document.write( "f(x)=x^3-3x^2+3x-9\r
\n" ); document.write( "\n" ); document.write( "If you are allowed to use a graphing calculator, you will see that the function has only one real zero, x=3.
\n" ); document.write( "(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.\r
\n" ); document.write( "\n" ); document.write( "ans:
\n" ); document.write( "one real zero=3
\n" ); document.write( "two imaginary zeros=+-sqrt(-3) or +-sqrt(3)i\r
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\n" ); document.write( "\n" ); document.write( " \"+graph%28+300%2C+300%2C+-5%2C+5%2C+-10%2C+10%2C+x%5E3-3x%5E2%2B3x-9%29+\"\r
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\n" ); document.write( "\n" ); document.write( "After reviewing my above solution, I realized the function could be factored:
\n" ); document.write( "x^3-3x^2+3x-9=x^2(x-3)+3(x-3)=(x-3)(x^2+3)
\n" ); document.write( "This would give you one real zero, 3 and two +-sqrt(-3), imaginary zeros, same as above.
\n" ); document.write( "This is the preferred method as you do not require a calculator for the solution. \n" ); document.write( "
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