SOLUTION: 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

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 .
RELATED QUESTIONS
algebra of linear and quadratic expressions. find the values of k for which the... (answered by jim_thompson5910)

"For what values of k will the equation x^2 + kx + 25 = 0 have no real... (answered by ikleyn)

show that the equations y=kx-1 and y=x^2+(k-1)x+k^2 have no real solution for all values... (answered by Edwin McCravy)

f(x) = x2 - kx + 9, where k is a constant find the set of values of k for which the... (answered by venugopalramana)

Hello, this is a question from my Algebra 2 textbook: Find all values of c for which... (answered by jim_thompson5910)

For the given matrix, the values of h and k are real constants. For which value of h and... (answered by ikleyn)

For what values of k will the equation kx^2+(k-2)x+4k=0 have no real... (answered by vleith)

Find values of c so that the equation will have two solutions, one solution, and no real... (answered by Nate)

Find all real solutions of the equation. (Enter your answers as a comma-separated list.... (answered by ewatrrr)