How do you find the discriminant of #7x^2+6x+2=0# and use it to determine if the equation has one, two real or two imaginary roots?
Consider the standard format of
The discriminant is the part of
If this is 0 then the vertex is actually on the on the axis so has 1 point
If this is negative then the roots are complex numbers
If this is positive and greater than 0 then it has two roots
Added comment: I have had people argue that when the discriminant is 0 there is still 2 roots but they are the same value. This condition is called duplicity.
I do not like this!
So for this equation:
The solutions are
The quadratic equation is
Here, we have
The discriminant is
The roots are imaginary