document.write( "Question 1184258: If the line y + 2x = p does not intersect the curve y^2 = x + p, find the range of values of p \n" ); document.write( "
Algebra.Com's Answer #814809 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We solve them simultaneously.  If the solutions are real, they will be the\r\n" );
document.write( "values at which they intersect, and if they are imaginary they will not\r\n" );
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document.write( "\"system%28y+%2B+2x+=+p%2Cy%5E2+=+x+%2B+p%29\"\r\n" );
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document.write( "Solve the first equation for y:\r\n" );
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document.write( "\"y=p-2x\"\r\n" );
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document.write( "Substitute in the second equation:\r\n" );
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document.write( "\"%28p-2x%29%5E2+=+x+%2B+p%29\"\r\n" );
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document.write( "\"p%5E2-4px%2B4x%5E2+=+x+%2B+p\"\r\n" );
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document.write( "\"4x%5E2-4px-x%2Bp%5E2-p=0\"\r\n" );
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document.write( "\"%284%29x%5E2%2B%28-4p-1%29x%2B%28p%5E2-p%29=0\"\r\n" );
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document.write( "\"x+=+%28%284p%2B1%29+%2B-+sqrt%28+%2816p%5E2%2B8p%2B1%29-16%28p%5E2-p%29+%29%29%2F8+\"\r\n" );
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document.write( "\"x+=+%28%284p%2B1%29+%2B-+sqrt%28+16p%5E2%2B8p%2B1-16p%5E2%2B16p+%29%29%2F8+\"\r\n" );
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document.write( "\"x+=+%28%284p%2B1%29+%2B-+sqrt%2824p%2B1%29%29%2F8+\"\r\n" );
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document.write( "That will not intersect when 24p+1 < 0, or when p < -1/24\r\n" );
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document.write( "Edwin
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