Check the discriminant, as it says. If it's positive, then you have 2 unequal real roots. If it's negative, no real roots. If it's 0, one root of multiplicity 2.
The discriminant is what's under the radical in the quadratic formula.
Use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution, or no solution, WITHOUT solving each equation below.
(1) x^2 + 5x + 7 = 0
(2) 2x^2 - 3x + 4 = 0
NOTE: What is the correct definition of a discriminant?