document.write( "Question 134785: if the roots of the quadratic equation $\"px%5E2%2Bqx%2Br=0\"$ differ by 4, show that $\"q%5E2=4p%284p%2Br%29\"$ . ThNK yOU for your help \n" ); document.write( "

Algebra.Com's Answer #98626 by solver91311(24713) $\"\"$ $\"About$

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Using the quadratic formula, the roots of $\"px%5E2%2Bqx%2Br=0\"$ are:\r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-q+%2B-+sqrt%28+q%5E2-4pr+%29%29%2F%282p%29+\"$ and these two roots differ by 4, so:\r
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\r
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\n" ); document.write( "\n" ); document.write( " $\"2%28sqrt%28+q%5E2-4pr+%29%29%2F%282p%29=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"sqrt%28+q%5E2-4pr+%29%2Fp=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"sqrt%28+q%5E2-4pr+%29=4p\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"q%5E2-4pr=16p%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"q%5E2=16p%5E2%2B4pr\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"q%5E2=4p%284p%2Br%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In general, if the roots differ by $\"d\"$ , then $\"q%5E2=dp%28dp%2Br%29\"$ \n" ); document.write( "

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