Determining the value of variables according to the number of roots

[Nise]

Determine the values of k for which the quadratic equation x^2+kx+9=0 will have:
a) Two equal roots
b) Two distinct roots
c) No roots
I'm not sure if I am correct but I came to the answer of 6 for part a by using the discriminant to solve for k when the equation equals 0
but I am not sure how to solve the other two questions. I know that when the discriminant is equal to less than 0 there will be no roots and when it is equal to greater than 0 there will be two distinct roots, but I am not sure how to solve and express this algebraically.
Any guidance would be greatly appreciated.

 

[Deleted member 4993]

Determine the values of k for which the quadratic equation x^2+kx+9=0 will have:
a) Two equal roots
b) Two distinct roots
c) No roots
I'm not sure if I am correct but I came to the answer of 6 for part a by using the discriminant to solve for k when the equation equals 0
but I am not sure how to solve the other two questions. I know that when the discriminant is equal to less than 0 there will be no roots and when it is equal to greater than 0 there will be two distinct roots, but I am not sure how to solve and express this algebraically.
Any guidance would be greatly appreciated.

discriminant = B² - 4AC = 0 ← equal roots

b) discriminant = B² - 4AC > 0 ← distinct roots

In your case:

A = 1 ; B = k ; C = 9

B² - 4AC > 0 → k² - 36 > 0 → k² > 36 → |k| > 6

Follow the same method for (c)