![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/step1.JPG\")
The solutions of a quadratic equation ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=e88fb4aee19f820030804b137d62b0b8.png\")
can be classified as follows. \ \
If the discriminant ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=8a04976a9fe5bfaa1f6eeb6c06d9c609.png\")
is \ \
1. positive, then the quadratic equation has two distinct real solutions and and its graph has two x - intercepts.
\2. zero, then the quadratic equation has one repeated real solution and its graph has one x - intercept.
\3. negative, then the quadratic equation has no real solutions and its graph has no x - intercepts.
\![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/step2.JPG\")
The quadratic equation is ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=12f520c2edd1f0dcf74d4cc85fdde60a.png\")
.
The general form of the quadratic equation is .
The discriminant formula is .
Consider .
Compare the above equation with general form of the quadratic equation.
\![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=d0fc0ab78b79503726972c9b9f426732.png\")
.
Substitute the values of in .
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=8a93818cd77a40f3630f0068e25b9b11.png\")
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=cd88a7a5ff4540fef167279236b4742e.png\")
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=40671a9032e612a15fd0a9e528b9f051.png\")
.
Since the discriminant is negative, the quadratic equation has no real solutions and its graph has no x - intercepts.
\![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/solution.JPG\")
The quadratic equation has no real solutions.