document.write( "Question 1132103: The roots of the equation x² + 2px + q = 0 differ by 2. Show that
\n" ); document.write( "p² = 1 + q \n" ); document.write( "

Algebra.Com's Answer #748997 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Let the roots be r and r+2. Vieta's Theorem tells us

\n" ); document.write( "(1) the sum of the roots is -2p: $\"-2p+=+r%2B%28r%2B2%29+=+2r%2B2\"$ --> $\"-p+=+r%2B1\"$ and
\n" ); document.write( "(2) the product of the roots is q: $\"q+=+r%28r%2B2%29+=+r%5E2%2B2r\"$

\n" ); document.write( "Then

\n" ); document.write( " $\"p%5E2+=+%28r%2B1%29%5E2+=+r%5E2%2B2r%2B1\"$ and
\n" ); document.write( " $\"q%2B1+=+r%5E2%2B2r%2B1\"$

\n" ); document.write( "And so p^2 = q+1. \n" ); document.write( "

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