document.write( "Question 983477: Find the polynomial with leading coefficient -2 that has degree 3 and roots 2 and 3i.. \n" ); document.write( "

Algebra.Com's Answer #604285 by MathLover1(20850) $\"\"$ $\"About$

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the polynomial with leading coefficient $\"-2\"$ that has degree $\"3\"$ and roots $\"x%5B1%5D=2\"$ and $\"x%5B2%5D=3i\"$ \r
\n" ); document.write( "\n" ); document.write( "if the polynomial has $\"x%5B2%5D=3i\"$ , then must have $\"x%5B3%5D=-3i\"$ because complex roots always come in pairs\r
\n" ); document.write( "\n" ); document.write( "use zero product formula:\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29\"$ ....since given that leading coefficient is $\"-2\"$ , multiply product above by

....substitute given roots\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-2%28%28x-2%29%28x-3i%29%28x-%28-3i%29%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-2%28%28x-2%29%28x-3i%29%28x%2B3i%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-2%28%28x-2%29%28x%5E2-%283i%29%5E2%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-2%28%28x-2%29%28x%5E2-9%28-1%29%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-2%28%28x-2%29%28x%5E2%2B9%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-2%28x%5E3%2B9x-2x%5E2-18%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-2x%5E3-18x%2B4x%5E2%2B36\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-2x%5E3%2B4x%5E2-18x%2B36\"$ \r
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