document.write( "Question 629356:
\r\n" ); document.write( "25 + 4x² = -20x\r\n" ); document.write( " discriminant\r\n" ); document.write( "how do you find the ~~determinant~~ then the number of rational, irrational or complex roots??

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

Algebra.Com's Answer #396225 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "25 + 4x² = -20x\r\n" );
document.write( "\r\n" );
document.write( "how do you find the determinant then the number of rational, irrational or complex roots??\r\n" );
document.write( "\r\n" );
document.write( "The word is \"discriminant\", not \"determinant\".\r\n" );
document.write( "\r\n" );
document.write( "First you get the quadratic equation in descending order with 0\r\n" );
document.write( "on the right.\r\n" );
document.write( "\r\n" );
document.write( "      25 + 4x² = -20x\r\n" );
document.write( "\r\n" );
document.write( "4x² + 20x + 25 = 0\r\n" );
document.write( "\r\n" );
document.write( "Compare that to the general quadratic equation:\r\n" );
document.write( "\r\n" );
document.write( " ax² + bx + c = 0\r\n" );
document.write( "\r\n" );
document.write( "If you remember the quadratic formula,  \r\n" );
document.write( "\r\n" );
document.write( "then you already know the discriminant formula because it is\r\n" );
document.write( "what is under the aquare root part of the quadratic formula.\r\n" );
document.write( "\r\n" );
document.write( "Discriminant = b² - 4ac      \r\n" );
document.write( "\r\n" );
document.write( "Comparing your equation to the general quadratic equation,\r\n" );
document.write( "\r\n" );
document.write( "a = 4, b = 20, c = 25\r\n" );
document.write( "\r\n" );
document.write( "Substitute in the discriminant formula:\r\n" );
document.write( "\r\n" );
document.write( "Discriminant = b² - 4ac \r\n" );
document.write( "\r\n" );
document.write( "Discriminant = (20)² - 4(4)(25)\r\n" );
document.write( "\r\n" );
document.write( "Discriminant = 400 - 400\r\n" );
document.write( "\r\n" );
document.write( "Discriminant = 0\r\n" );
document.write( "\r\n" );
document.write( "The rules are\r\n" );
document.write( "\r\n" );
document.write( "1. If the discriminant is positive there are 2 real roots\r\n" );
document.write( "   A.  If the discriminant is a perfect square, both roots are rational\r\n" );
document.write( "   B.  If the discriminant is not a perfect square, both roots are irrational.\r\n" );
document.write( "2. If the discriminant is negative, there are 2 conjugate complex roots.\r\n" );
document.write( "3. If the discriminant is 0, there is just one real rational root.\r\n" );
document.write( "\r\n" );
document.write( "Your problem is case 3, so there is one real rational root. \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );