The necessary and sufficient condition for it is that the discriminant of the equation must be negative:
d = < 0, i.e.
(-6)^2 - 4*a*3 < 0,
36 < 12a,
a > 3.
See the plots below for a = 2, 3 and 4.
Plot y1 = (red), y2 = (green), y3 = (blue)
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website! An -intercept is the point where a parabola crosses the x-axis. This point is also known as a , , or .
the expression , called the "", and we can use it to find out what kind and how many roots the quadratic function have
rule:
if , Discriminant is greater than zero, Positive Discriminant: Solutions
if , Discriminant is equal to zero. Solution
if , Discriminant is less than zero ,Negative Discriminant: Solutions => means -intercepts
so, you will use for
since , , and , you have
check:
if , we can use and see the graph of
as you can see, there is no x-intercept