Case 2.
If the whole graph lies on one side of the x-axis , then the curve
never touched the x-axis, never crossed it either. There are no real
roots (but there are complex roots of the corresponding quadratic
equation and they always come in matched pairs called complex
conjugates).
Analytically, this corresponds to
negative
values of the
discrimi-
D < 0
nant, (
)
10
8
2
f (x) = 3x
9x + 10
6
f x
4
a > 0
2
D < 0
0
0
0.5
1
1.5
2
2.5
3
x
0
2
2
f (x) =
3x
+9x 10
4
f x
a < 0
6
D < 0
8
0
0.5
1
1.5
2
2.5
3
x
5