document.write( "Question 966986: If one root of 5x^2+13x+p=0 be reciprocal of the other then the value of p is \n" ); document.write( "
Algebra.Com's Answer #591132 by KMST(5328)\"\" \"About 
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If the roots of \"5x%5E2%2B13x%2Bp=0\" are \"r\" and \"1%2Fr\" ,
\n" ); document.write( "then we can \"factorize\" \"5x%5E2%2B13x%2Bp\" like this
\n" ); document.write( "\"5x%5E2%2B13x%2Bp=5%28x-r%29%28x-1%2Fr%29\" ,
\n" ); document.write( "and if we multiply the two expressions in brackets, we get
\n" ); document.write( " .
\n" ); document.write( "So, since that is true for all values of x,
\n" ); document.write( "the coefficients must be the equal, meaning that
\n" ); document.write( "\"highlight%28p=5%29\" ,
\n" ); document.write( "and \"13=-5%281%2Fr%2Br%29\" .
\n" ); document.write( "We can find those reciprocal roots,
\n" ); document.write( "or at least prove that there are real roots,
\n" ); document.write( "to make sure we have not been tricked.
\n" ); document.write( "It turns out that the determinant for \"5x%5E2%2B13x%2B5=0\" is
\n" ); document.write( "\"13%5E3-4%2A5%2A5=169-100%3E0\" and there are real roots given by
\n" ); document.write( "\"x=%28-13+%2B-+sqrt%2869%29%29%2F10\" . \n" ); document.write( "
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