solve the equation in perhaps ?
x^2+6x+9m=0
talk about the sign.
for m>1 , m=1, m<1
Graphic.
We have
Intersect the graph of with parallel lines to x-axis with equation
If then the line doesn't intersect the graph.
If the line is tangent to the graph and the equation has a double solution
If the line intersects the graph in 2 points and the equation has two negative solutions.
If then the equation has the solutions
If then the equation has one negative solution and one positive solution.