document.write( "Question 1019659: Find the values of p for which the graph of
\n" ); document.write( " y=px^2+8x+p-6y
\n" ); document.write( "crosses the x-axis. \n" ); document.write( "

Algebra.Com's Answer #635619 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
It is strange to have $\"y\"$ on both sides of the equal sign.
\n" ); document.write( "If you did post correctly,
\n" ); document.write( " $\"y=px%5E2%2B8x%2Bp-6y\"$
\n" ); document.write( " $\"y%2B6y=px%5E2%2B8x%2Bp\"$
\n" ); document.write( " $\"7y=px%5E2%2B8x%2Bp\"$ <--> $\"y=%28px%5E2%2B8x%2Bp%29%2F7\"$ <--> $\"y=%28p%2F7%29x%5E2%2B%288%2F7%29x%2Bp%2F7\"$
\n" ); document.write( "If the graph of that quadratic function crosses the $\"y=0%7D%7D+x-axis%2C%0D%0Ait+will+do+it+at+two+values+of+%7B%7B%7Bx\"$ ,
\n" ); document.write( "meaning that $\"y=0\"$ will give two distinct solutions for $\"x\"$ .
\n" ); document.write( "That means $\"px%5E2%2B8x%2Bp=0\"$ has two distinct solutions for $\"x\"$ .
\n" ); document.write( "If a quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ has two distinct solutions for $\"x\"$ ,
\n" ); document.write( "it means that the discriminant is positive:
\n" ); document.write( " $\"b%5E2-4ac%3E0\"$ .
\n" ); document.write( "In this case, that would be
\n" ); document.write( " $\"8%5E2-4%2Ap%2Ap%3E0\"$
\n" ); document.write( " $\"64-4p%5E2%3E0\"$
\n" ); document.write( " $\"16-p%5E2%3E0\"$
\n" ); document.write( " $\"16%3Ep%5E2\"$
\n" ); document.write( " $\"highlight%28-4%3Cp%3C4%29\"$ \n" ); document.write( "

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