Use the discriminant to determine the number and types of solutions to a quadratic equation.
The discriminant is the value b^2 - 4ac when the quadratic is in standard form: ax^2 + bx + c = 0
If the discriminant is a positive perfect square, you have 2 real rational roots (solutions).
If the discriminant is a positive number that is not a perfect square, you will have 2 real irrational roots (solutions).
If the discriminant is a negative number, you have 2 complex solutions, NO real roots (solutions)
If the discriminant is zero, you have 1 real rational root (solution). Also called a double root.
b^2 - 4ac = 5^2 - 4*1*7 =
25 - 28 = -3
NO real solutions