document.write( "Question 199851: Hi!\r
\n" ); document.write( "\n" ); document.write( "Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions.\r
\n" ); document.write( "\n" ); document.write( "S has degree 4, and zeros 3i and 4i\r
\n" ); document.write( "\n" ); document.write( "thanks for your help! \n" ); document.write( "

Algebra.Com's Answer #150231 by solver91311(24713) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "See the answer to Question 199809.\r
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\n" ); document.write( "\n" ); document.write( "http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.199809.html\r
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\n" ); document.write( "\n" ); document.write( "Here you are looking for a polynomial of degree 4, and you are given that two of the four zeros are

and

, which, expressed in complex number form are

and

. But recall that complex roots always occur in conjugate pairs, therefore the other two zeros are

and

. Hence the four factors of the desired polynomial are:\r
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\r
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\n" ); document.write( "\n" ); document.write( "Hint: Each of the two pairs of conjugates will result in a difference of two squares binomial, and remember that

\r
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\n" ); document.write( "\n" ); document.write( "John
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