document.write( "Question 313233: Describe the nature of the roots of the following quadratic: y=x^2-3x-9 \n" ); document.write( "

Algebra.Com's Answer #224051 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For any quadratic polynomial equation of the form:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Find the Discriminant,

and evaluate the nature of the roots as follows:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

0 \ \ \Rightarrow\ \\"> Two real and unequal roots. If

is a perfect square, the quadratic factors over

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

Two real and equal roots. Alternatively, one real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

A conjugate pair of complex roots of the form

where

is the imaginary number defined by

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

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

\n" );