Question 235130: Solving Quadratic Equations by graphing; there is either 1, 2, or no real solutions... can you help me with this?
x^2-2x-24=0 Answer by solver91311(5072) (Show Source):
Then you want to find the one place that the graph of the function is tangent to the -axis, meaning that you have 1 real solution (actually, you would say that the equation has one real root with a multiplicity of two), or you want to find the two places that the graph intersects the -axis, meaning that you have two distinct real solutions, or you want to discover that the graph never touches the -axis, meaning that the equation has no real solutions.
What you are doing is answering the question, "What number or numbers can I substitute for so that ?" The function has a value of zero at the -axis.
Compare this to:
Notice two things: 1. The function is a perfect square trinomial. 2. The graph is tangent to the axis. One root with a multiplicity of 2.
No compare to:
Notice that the graph does not touch the -axis at all. No real solutions.
