document.write( "Question 86425: can anyone help me with this question: find a polynomial with integer coefficients that has the given zeros 3, 3+i \n" ); document.write( "
Algebra.Com's Answer #62619 by ankor@dixie-net.com(22740)\"\" \"About 
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can anyone help me with this question: find a polynomial with integer coefficients that has the given zeros 3, 3+i
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\n" ); document.write( "First factor is easy:
\n" ); document.write( "x = 3
\n" ); document.write( "1st factor is: (x-3)= 0
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\n" ); document.write( "x = 3 + i
\n" ); document.write( "Think of it as the reverse of completing the square
\n" ); document.write( "x - 3 = i
\n" ); document.write( "Square both sides
\n" ); document.write( "(x-3)^2 = i^2;
\n" ); document.write( "x^2 - 6x + 9 = -1: FOILed (x-3(x-3); we know that i^2 = -1
\n" ); document.write( "x^2 - 6x + 9 + 1 = 0
\n" ); document.write( "x^2 - 6x + 10 = 0; is the 2nd factor
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\n" ); document.write( "Multiply the two factors the long way:
\n" ); document.write( "(x-3) * (x^2 - 6x + 10) = x^3 - 9x^2 + 28x - 30 is the polynomial
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\n" ); document.write( "Did this help? \n" ); document.write( "
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