Parabola , finding the discriminant

Question

h(t)=-3 t^(2)+122

I am trying to understand discriminant and what they mean

If I plug my numbers into the equation

ax^2+bx+c=0

3(3) + 0 - 122 = -113

Does that mean my discriminant is 0 because I dont have a (B)?

and because the outcome of the equation is negative, I only have 1 real solution?

Answer 1

Let a = -3, b = 0, and c = 122. Then we can plug them in the discriminant.

b² - 4ac = 0² - 4(-3)(122) = 1464

Since the discriminant is positive, there are 2 real solutions.

b² - 4ac > 0 means there are 2 real solutions.

b² - 4ac = 0 means there is 1 real solution.

b² - 4ac < 0 means there are no real solutions.

Note: The leading coefficients don't relate to the number of types of solutions.