document.write( "Question 1207338: Show that x^2 + 4 is prime. \n" ); document.write( "

Algebra.Com's Answer #845166 by ikleyn(52800) $\"\"$ $\"About$

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\n" ); document.write( "Show that x^2 + 4 is prime.
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document.write( "If the given polynomial  be a composite polynomial, it would be a product of linear polynomials\r\n" );
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document.write( "     = (ax+b)*(cx+d).\r\n" );
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document.write( "In this case, it would have two roots,    and  .\r\n" );
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document.write( "But from the other side, this polynomial    is always positive over real numbers and has no real roots.\r\n" );
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document.write( "This contradiction PROVES that the given polynomial is a PRIME polynomial.\r\n" );
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document.write( "We proved that this polynomial is prime not only over the ring of integer numbers, \r\n" );
document.write( "but even over the much wider field of real numbers (!).\r\n" );
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