document.write( "Question 1102632: Find the value of k in x^4-4x^2+k that gives 4 complex zeros. \n" ); document.write( "

Algebra.Com's Answer #717382 by ikleyn(52817) $\"\"$ $\"About$

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document.write( "The necessary and sufficient condition for it is THIS:\r\n" );
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document.write( "    The polynomial (the function)  x^4 - 4x^2 + k  is always positive (and never zero or negative).\r\n" );
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document.write( "In turn, the necessary and sufficient condition for it is THIS:\r\n" );
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document.write( "    The polynomial  y^2 -4y + k  is always positive.\r\n" );
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document.write( "In turn, the necessary and sufficient condition for it is THIS:\r\n" );
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document.write( "    The discriminant  d = 4^2 - 4k is negative:\r\n" );
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document.write( "    16 - 4k < 0  ====>  16 < 4k  ====>  4 < k.\r\n" );
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document.write( "Answer.  k > 4.\r\n" );
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