document.write( "Question 1041330: What are the negative and positive intervals to these equations?
\n" ); document.write( "y=x^2+5x+6
\n" ); document.write( "y=2x^2-11x-5
\n" ); document.write( "

Algebra.Com's Answer #656301 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "What are the negative and positive intervals to these equations?
\n" ); document.write( "y=x^2+5x+6
\n" ); document.write( "y=2x^2-11x-5
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "1.  y = \"x%5E2+%2B+5x+%2B+6\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Find the roots of the polynomial. For it, factorize the polynomial:\r\n" );
document.write( "\r\n" );
document.write( "    \"x%5E2+%2B+5x+%2B+6\" = (x+2)*(x+3).\r\n" );
document.write( "\r\n" );
document.write( "    So, the roots are x = -3  and  x = -2.\r\n" );
document.write( "\r\n" );
document.write( "    The polynomial is negative when  -3 < x < -2, i.e in the interval (-3,-2).\r\n" );
document.write( "\r\n" );
document.write( "    The polynomial is positive when  x < -3  or  x > -2, i.e. in the the union of two semi-infinite intervals  (\"-infinity\",\"-3\") U (\"-2\",\"infinity\").\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  Now make the same with the second equation.\r\n" );
document.write( "\r\n" );
document.write( "    First find its roots (you can use the quadratic formula).\r\n" );
document.write( "\r\n" );
document.write( "    Then analyse the sign of the polynomial between the roots, to the left of the roots and to the right of the roots.\r\n" );
document.write( "

\n" ); document.write( "
\n" ); document.write( "
\n" );