document.write( "Question 1177234: Determine the signs of the roots of the equation (if they exist) without solving the equation:
\n" ); document.write( "\"x%5E2-2x-1=0\"
\n" ); document.write( "Found the discriminant (8)
\n" ); document.write( "But apparently the answer isn't 2 positive roots, so I'm stuck \n" ); document.write( "
Algebra.Com's Answer #805547 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The discriminant of the equation   d = b^2 - 4ac = (-2)^2 + 4*1*(-1) = 4 + 4 = 8   is a positive real number,\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so the roots are real numbers.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Next,  according to the  Vieta's theorem,  the product of the roots is equal to the constant term,  which is  -1  in this case,\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so the roots are of opposite signs:  one root is a positive real number,  while another root is a negative real number.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "That's all.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solved,  answered,  explained and completed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );