document.write( "Question 38047: My teacher has our advanced algebra class taking college algebra tests just for the heck of it.
\n" ); document.write( "The problem asks to find a polynomial equation of degree 4 with integral coefficients that has solutions 1+i, 3, 0. \n" ); document.write( "

Algebra.Com's Answer #23545 by fractalier(6550) $\"\"$ $\"About$

You can put this solution on YOUR website!
Well one thing you have to recognize is that complex roots ALWAYS come in conjugate pairs...so that if 1 + i is a root, so is 1 - i, even if they don't give it to you...thus our polynomial must be
\n" ); document.write( "(x - 0)(x - 3)(x - (1 + i))(x - (1 - i)) = 0
\n" ); document.write( "now multiply it all out
\n" ); document.write( "(x^2 - 3x)(x - 1 + i)(x - 1 - i) = 0
\n" ); document.write( "(x^2 - 3x)(x^2 - 2x + 2) = 0
\n" ); document.write( "x^4 - 5x^3 + 8x^2 - 6x = 0 \n" ); document.write( "

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