document.write( "Question 1098020: Find a polynomial of lowest degree with rational coefficients that has 3 and 4i as some of its zeros. \n" ); document.write( "

Algebra.Com's Answer #712448 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "For polynomials with real coefficients, complex roots \"z\" always go in pairs \r\n" );
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document.write( "(z, z-conjugated).\r\n" );
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document.write( "The conjugated to  4i  is the complex number  -4i.\r\n" );
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document.write( "So, your polynomial is  a*(x-3)*(x-4i)*(x+4i) = .\r\n" );
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document.write( "The leading coefficient \"a\" is an arbitrary real number, or, \r\n" );
document.write( "if you really are seeking for rational coefficients, then \"a\" must be a rational number.\r\n" );
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