document.write( "Question 678195: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros: -2, 3+i \r
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Algebra.Com's Answer #421210 by nerdybill(7384)\"\" \"About 
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Find a polynomial f(x) of degree 3 with real coefficients and the following zeros: -2, 3+i
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\n" ); document.write( "If a zero has an \"imaginary\" root such as:
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\n" ); document.write( "then, there must be another imaginary root that is the conjugate:
\n" ); document.write( "3-i
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\n" ); document.write( "so, all the zeros are:
\n" ); document.write( "-2, 3+i , 3-i
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\n" ); document.write( "The factors must be:
\n" ); document.write( "(x - (-2)) , (x - (3+i)) , (x - (3-i))
\n" ); document.write( "(x+2) , (x-3-i) , (x-3+i)
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\n" ); document.write( "Multiply the factors together to get the polynomial:
\n" ); document.write( "(x+2)(x-3-i)(x-3+i)
\n" ); document.write( "(x+2)(x(x-3+i)-3(x-3+i)-i(x-3+i))
\n" ); document.write( "(x+2)((x^2-3x+xi)-(3x-9+3i)-(xi-3i+i^2))
\n" ); document.write( "(x+2)((x^2-3x+xi)-(3x-9+3i)-(xi-3i-1))
\n" ); document.write( "(x+2)(x^2-3x+xi-3x+9-3i-xi+3i+1)
\n" ); document.write( "(x+2)(x^2-6x+xi+9-3i-xi+3i+1)
\n" ); document.write( "(x+2)(x^2-6x+9-3i+3i+1)
\n" ); document.write( "(x+2)(x^2-6x+9+1)
\n" ); document.write( "(x+2)(x^2-6x+10)
\n" ); document.write( "x(x^2-6x+10)+2(x^2-6x+10)
\n" ); document.write( "(x^3-6x^2+10x)+(2x^2-12x+20)
\n" ); document.write( "x^3-6x^2+10x+2x^2-12x+20
\n" ); document.write( "x^3-4x^2+10x-12x+20
\n" ); document.write( "x^3-4x^2-2x+20\r
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