Calculate the discriminant of a quadratic equation and identify the nature of its roots.
Last updated: June 2026 | By Patchworkr Team
Coefficient a cannot be blank.
For the quadratic equation ax^2 + bx + c = 0, the discriminant is D = b^2 - 4ac.
Since D > 0, the equation has two distinct real roots.
What if D is positive?
A positive discriminant means the quadratic has two distinct real roots.
What if D is zero?
A zero discriminant means the quadratic has one repeated real root.
What if D is negative?
A negative discriminant means the quadratic has two complex roots.
Does a have to be nonzero?
Yes. If a is zero, the equation is not quadratic and the discriminant is not meaningful here.
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