document.write( "Question 1209309: Find all real values of p such that
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Algebra.Com's Answer #848213 by ikleyn(52778)\"\" \"About 
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document.write( "Expression  2(x+6)(x-p)  represents a parabola opened upward\r\n" );
document.write( "with the vertex  at  x= \"%28-6%2Bp%29%2F2\",  half-way between x-intercepts -6 and p.\r\n" );
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document.write( "The y-value at the vertex is  \r\n" );
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document.write( "    \"2%2A%28%28-6%2Bp%29%2F2%2B6%29%2A%28%28-6%2Bp%29%2F2-p%29\" = \"2%2A%28%286%2Bp%29%2F2%29%28%28-6-p%29%2F2%29\" = \"-%281%2F2%29%2A%286%2Bp%29%5E2\".\r\n" );
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document.write( "We want\r\n" );
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document.write( "    \"-%281%2F2%29%2A%286%2Bp%29%5E2\" = -4.\r\n" );
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document.write( "It gives  \r\n" );
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document.write( "    \"%286%2Bp%29%5E2\" = 8\r\n" );
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document.write( "    6 + p = +/- \"sqrt%288%29\"\r\n" );
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document.write( "    p = -6 +/- \"2%2Asqrt%282%29\".\r\n" );
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document.write( "ANSWER.  There are two real numbers \"p\" satisfying the imposed requirements.\r\n" );
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document.write( "         They are  -6 - \"2%2Asqrt%282%29\"  and  -6 + \"2%2Asqrt%282%29\".\r\n" );
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