By definition, the roots of a quadratic function can be found using an equation of the form:
[tex]x = \frac{-b+/-\sqrt{b^2 - 4ac}}{2a} [/tex]
The discriminant is the following part of the expression:
[tex]b^2 - 4ac[/tex]
Therefore, we have three cases:
Case 1:
[tex]b ^ 2 - 4ac\ \textgreater \ 0
[/tex]
Then there are two real solutions
Case 2:
[tex]b ^ 2 - 4ac = 0
[/tex]
Then there is a real solution with multiplicity two
Case 3:
[tex]b ^ 2 - 4ac \ \textless \ 0
[/tex]
There are no real solutions
When the graph of a quadratic equation has no cut points with the x axis, then we are in case number 3.
Answer:
B. Negative
[tex]b ^ 2 - 4ac \ \textless \ 0
[/tex]
