SOLUTION: 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
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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(24713) (Show Source): You can put this solution on YOUR website!
First you want to graph the function \ =\ y\ =\ x^2\ -\ 2x\ -\ 24)
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 \ =\ 0)
?" The function has a value of zero at the -axis.
Compare this to: \ =\ y\ =\ x^2\ -\ 2x\ +\ 1)
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: \ =\ y\ =\ x^2\ -\ 2x\ +\ 4)
Notice that the graph does not touch the -axis at all. No real solutions.
John
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