document.write( "Question 997738: I need to see the steps to solve:\r
\n" ); document.write( "\n" ); document.write( "Find the cubic equation that has -1 and 2i as roots.\r
\n" ); document.write( "\n" ); document.write( "Thank you. \n" ); document.write( "
Algebra.Com's Answer #615695 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
imaginary or complex roots come in pairs as best i can remember.
\n" ); document.write( "your roots are x = -1, x = +2i, x = -2i
\n" ); document.write( "your factors are (x+1), (x-2i), (x+2i)
\n" ); document.write( "(x - 2i) * (x + 2i) = x^2 + 2ix - 2ix -4i^2
\n" ); document.write( "the + 2ix and the - 2ix cancel out and you are left with:
\n" ); document.write( "x^2 - 4i^2
\n" ); document.write( "since i^2 = -1, you are left with:
\n" ); document.write( "x^2 -4*-1 which is equal to:
\n" ); document.write( "x^2 + 4
\n" ); document.write( "now you multiply this by (x + 1) to get:
\n" ); document.write( "(x + 1) * (x^2 + 4) = x^3 + 4x + x^2 + 4
\n" ); document.write( "combine like terms and order the terms in descending order to get:
\n" ); document.write( "x^2 + x^2 + 4x + 4
\n" ); document.write( "that should be your cubic equation.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "here's a reference on complex roots.
\n" ); document.write( "there are numerous others on the web.
\n" ); document.write( "https://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html\r
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