document.write( "Question 1127899: Find the values of b such that the equation below always gives real solutions.
\n" ); document.write( "-3x^2 + bx -1 = 0 \n" ); document.write( "
Algebra.Com's Answer #744368 by ikleyn(52781)\"\" \"About 
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document.write( "To satisfy the problem's requirement, the discriminant of the equation must be non-negative:\r\n" );
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document.write( "\"b%5E2+-+4ac\" >= 0,\r\n" );
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document.write( "\"b%5E2+-+4%2A%28-3%29%2A%28-1%29\" >= 0,\r\n" );
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document.write( "\"b%5E2+-+12\" >= 0,\r\n" );
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document.write( "\"b%5E2\" >= 12  ====>   b >= \"sqrt%2812%29\" = \"2%2Asqrt%283%29\"   OR   b <= -\"sqrt%2812%29\" = \"-2%2Asqrt%283%29\".\r\n" );
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document.write( "Answer.  The necessary and sufficient condition for \"b\"  is  |b| >= \"2%2Asqrt%283%29\" =~ 3.464102 .\r\n" );
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