document.write( "Question 1193191: Find a polynomial f(x) of degree 4 with real coefficients and the following zeros.\r
\n" ); document.write( "\n" ); document.write( "1, (multiplicity 2), -2 +3i \n" ); document.write( "

Algebra.Com's Answer #825202 by MathLover1(20850) $\"\"$ $\"About$

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Find a polynomial f(x) of degree 4 with real coefficients and the following zeros.
\n" ); document.write( "1, (multiplicity 2), -2 +3i\r
\n" ); document.write( "\n" ); document.write( "given: degree $\"4+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29\"$ \r
\n" ); document.write( "\n" ); document.write( "zeros:
\n" ); document.write( " $\"x%5B1%5D=1\"$ ......... (multiplicity 2)
\n" ); document.write( " $\"x%5B2%5D=-2%2B3i\"$ -> then we also have $\"x%5B3%5D=-2-3i\"$ (complex roots always come in pairs)\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=%28x-1%29%28x-1%29%28x-%28-2%2B3i%29%29%28x-%28-2-3i%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=%28x-1%29%5E2%28x%2B2-3i%29%28x%2B2%2B3i%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=%28x%5E2+-+2x+%2B+1%29%28x%5E2%2B2x%2B3i%2Ax%2B2x%2B4%2B6i-3i%2Ax-6i-9i%5E2%29\"$ .....simplify\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=%28x%5E2+-+2x+%2B+1%29%28x%5E2+%2B+4+x+%2B+13%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=x%5E4+%2B+2x%5E3+%2B+6x%5E2+-+22x+%2B+13\"$ \r
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