Nature of roots of quadratic equations: The discriminant

Topic Notes
The discriminant is actually part of the quadratic formula. It is super useful when we only need to determine whether a quadratic equation has 2 real solutions, 1 real solution, or 2 complex solutions.
• For the quadratic equation: ax2+bx+c=0a{x^2} + bx + c = 0
quadratic formula: x=−b±b2−4ac    2ax = \frac{{ - b \pm \sqrt {{b^2} - 4ac\;} \;}}{{2a}}

• discriminant: b² - 4ac
The discriminant (△\vartriangle), b² - 4ac, can be used to discriminate between the different types of solutions:
if b2−4acb^2 - 4ac > 0 : 2 solutions (2 real solutions)
if b2−4acb^2 - 4ac = 0 : 1 solution (1 real solution)
if b2−4acb^2 - 4ac < 0 : no solution (2 complex solutions)
Basic Concepts
Related Concepts