![\"\"](\"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=b21681153861472247f85cc5fe75b1a7.png\")
.
The general form of quadratic equation is .
The discriminant formula is .
Consider .
Compare it with general form.
\![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=3a298904a22142f682414a61e4ea8658.png\")
Substitute the values of in ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=8a04976a9fe5bfaa1f6eeb6c06d9c609.png\")
.
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=2dfc5629c1a35e85ea3222b214b4b398.png\")
![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=1da262c9d2dbb4955ab239e860a083fb.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.