document.write( "Question 238424: Determine the values of p for which one root of the equation
\n" ); document.write( "x2 - 12x + p = 0 (x2 = x squared)
\n" ); document.write( "is 2 more than the other root.\r
\n" ); document.write( "\n" ); document.write( "Many thanks.\r
\n" ); document.write( "\n" ); document.write( "Walker \n" ); document.write( "

Algebra.Com's Answer #175181 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
The key to this problem is to understand that is some number, call it \"r\", is a root then (x-r) is a factor. So we are looking for an equation of the form:
\n" ); document.write( " $\"%28x+-+r%5B1%5D%29%28x+-+r%5B2%5D%29+-+0\"$
\n" ); document.write( "that simplifies to
\n" ); document.write( " $\"x%5E2+-12x+%2B+p+=+0\"$
\n" ); document.write( "and where $\"r%5B1%5D+=+r%5B2%5D+%2B+2\"$

\n" ); document.write( "Fortunately expressions of the form:
\n" ); document.write( " $\"x%5E2+%2Bbx+%2B+c\"$ are fairly simple to factor. We just look for the factors of \"c\" that add up to \"b\". So in your equation we look for a \"p\" whose factors add up to -12 and whose factors are 2 apart from each other. With some thought and/or trial and error we should be able to find that -5 and -7 are two apart from each other and they add up to -12. Since \"p\" is the product of these two factors, \"p\" is (-5)(-7) = 35. The final equation is:
\n" ); document.write( " $\"x%5E2+-12x+%2B+35+=+0\"$ whose roots are (-5) and (-7). \n" ); document.write( "

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