document.write( "Question 1122436: Find all solutions to x^4 - 7x + 12 =0 \n" ); document.write( "

Algebra.Com's Answer #738571 by ikleyn(52915) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Plot y = \r\n" );
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document.write( "This plot is a  HINT.  It shows you visually that there are no real solutions.\r\n" );
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document.write( "To prove it, use Calculus.\r\n" );
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document.write( "The Calculus will show you, first, that the polynomial has only one min/max point, where the first derivative is zero.\r\n" );
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document.write( "Next, since the polynomial tends to +infinity wnen  x--->   and/or  x ---> , it becomes clear that the min/max is actually the minimum.\r\n" );
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document.write( "Finally, you can check that the minimum provides a positive value of the polynomial.  //  It is a simple calculation.\r\n" );
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document.write( "Thus you (actually, it was me) proved that the given equation has no real solution.\r\n" );
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