document.write( "Question 1135104: Show that $\"f%28x%29=x%5E2%2B6x%2B12\"$ is always positive for all values of x \n" ); document.write( "

Algebra.Com's Answer #752654 by ikleyn(52786) $\"\"$ $\"About$

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document.write( " =  + 3 =  + 3.\r\n" );
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document.write( "So, this expression is the sum of two terms.\r\n" );
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document.write( "First term is quadratic binomial  ,  which ALWAYS is non-negative as a square of a real number.\r\n" );
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document.write( "The second term is constant term \"3\", which is positive, too.\r\n" );
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document.write( "Therefore, their sum is ALWAYS positive.\r\n" );
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document.write( "Thus, the original expression is always positive, too.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a TEMPLATE and a SAMPLE to you on how this and similar problems should be solved and worded.\r
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\n" ); document.write( "\n" ); document.write( "The method which I used is called \"completing the square\".\r
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\n" ); document.write( "\n" ); document.write( "On how this method works, you can read from the lesson\r
\n" ); document.write( "\n" ); document.write( " - HOW TO complete the square - Learning by examples \r
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\n" ); document.write( "\n" ); document.write( "Do not forget to post your \"Thanks\" to me after completing reading my post.\r
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