Question 348125: given the equation x^2 +kx +2=0 find all possible values of k for one real solution, 2 real solutions, and no real solutions Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! In the general form of the quadratic equaiton, , the value of the discriminant, , will indicate the number of real solutions:
means one real solution.
means two real solutions.
means no real solutions.
Your discriminant is:
So if you get one real solution. Solving this for k will tell us the k's that will result in one real solution. Adding 8 to each side we get:
This gives us or
For either of these values of k, there will be one real solution.
For two real solutions we want . This means we need . In other words, or .
For no real solutions we want . This means we need . In other words, and .
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