document.write( "Question 858686: For which values of P will x^2+p+x=3(x+1) have real roots \n" ); document.write( "

Algebra.Com's Answer #517325 by LinnW(1048) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%5E2%2Bp%2Bx=3%28x%2B1%29\"$
\n" ); document.write( "x^2 + p + x = 3x + 3
\n" ); document.write( "add -3x -3 to each side
\n" ); document.write( "x^2 -2x -3 + p
\n" ); document.write( "Determine whether roots are real by
\n" ); document.write( "seeing if $\"%28b%5E2+-4ac%29%3E=0\"$ where
\n" ); document.write( "a = 1 , b = -2 , c = ( -3 + p)
\n" ); document.write( " $\"%284+-+4%281%29%28-3+%2B+p%29+%29\"$
\n" ); document.write( " $\"%284+-+4%28-3+%2B+p%29+%29\"$
\n" ); document.write( " $\"%284+%2B+12+-+4p+%29\"$
\n" ); document.write( " $\"%28-+4p+%2B+16+%29\"$
\n" ); document.write( "When - 4p + 16 > 0 we have real roots
\n" ); document.write( "add -16 to each side
\n" ); document.write( " -4p > -16
\n" ); document.write( "divide each side by -4
\n" ); document.write( " p < 4
\n" ); document.write( " \n" ); document.write( "

\n" );