Okay, here we have this:
Considering the provided discriminants, we are going to identify what it indicates about the number of roots of the quadratic equation. So we obtain the following:
Let us remember that in an equation if the discriminant is negative, then there are no real solutions of the equation, if the discriminant is zero, there is only one solution and if the discriminant is positive, then it means that it obtains two solutions. According to this we have:
a) b²-4ac=5:
Since the discriminant is positive, then it means that it has two solutions.
b. b² - 4ac = 0
Since the discriminant is zero, then it means that it has only one solution.
c. b²-4ac = -10
Since the discriminant is negative, then it means that there are no real solutions to the equation