document.write( "Question 136630This question is from textbook Prentice Hall Algebra 2
\n" ); document.write( ": Find a fourth-degree polynomial equation with integer coefficients that has the given numbers as roots.\r
\n" ); document.write( "\n" ); document.write( "The given numbers are 3+ i and -2i \n" ); document.write( "

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If a polynomial equation has a complex root of the form $\"a%2Bbi\"$ , then the conjugate of the complex number, $\"a-bi\"$ is also a root. Therefore, your four roots are $\"3%2Bi\"$ , $\"3-i\"$ , $\"0-2i\"$ , and $\"0%2B2i\"$ \r
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\n" ); document.write( "\n" ); document.write( "If any number a is a root of a polynomial equation, then $\"x-a\"$ is a factor of the polynomial. Therefore, the factors of your polynomial are $\"x-%283%2Bi%29\"$ , $\"x-%283-i%29\"$ , $\"x-%28-2i%29\"$ , and $\"x-2i\"$ . Just multiply the 4 factors together and you will have your required polynomial. The problem asks for a polynomial equation so remember to set the 4th degree polynomial result equal to 0 at the end.\r
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\n" ); document.write( "\n" ); document.write( "Hint: Be very careful with your signs when multiplying. Remember that $\"i%5E2=-1\"$ , so something like $\"%28-2i%29%282i%29=-4%28-1%29=4\"$ .\r
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