document.write( "Question 200465: Quadratic equation: Why do you think the discriminant works. \n" ); document.write( "
Algebra.Com's Answer #150988 by RAY100(1637)\"\" \"About 
You can put this solution on YOUR website!
The Quadratic Formula is the answer to
\n" ); document.write( ".
\n" ); document.write( "ax^2 +bx + c =0,,,,,, most books have a derivation
\n" ); document.write( ".
\n" ); document.write( "as to why the Discriminant (D) works, let's look at quadratic answer
\n" ); document.write( ".
\n" ); document.write( "x= [ - (b) +/- sqrt { (b^2) - 4 (a) (c) } ] / 2a
\n" ); document.write( ".
\n" ); document.write( "or,,,,x= [-(b) +/- sqrt D ] / 2a
\n" ); document.write( ".
\n" ); document.write( "there are 3 conditions for the discriminant (D)
\n" ); document.write( ".
\n" ); document.write( "(1) D =0,,,,then x=[ -(b) +/- sqrt(0) ] /2a = -b/2a,,,,,therefore one answer
\n" ); document.write( ".
\n" ); document.write( "(2) D>0,,,,,,then x= [ -(b) +/- sqrt D ] /2a or x= [-(b) + sqrtD]/2a,,and x = [-b -sqrtD] /2a,,, or two answers
\n" ); document.write( ".
\n" ); document.write( "(3) D less than 0,,,,,,then x=[ -(b) +/- sqrt D ] /2a = [-b +/-sqrt (-#) ] /2a ,,,and with sqrt of a negative number, the answer is a complex number, not a real number,,,,,,therefore NO real number answers
\n" ); document.write( ". \n" ); document.write( "
\n" );