Quadratic Formula Calculator
The quadratic formula in action.
Quadratic Formula Calculator
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Calculated instantly
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What This Calculator Does
The Quadratic Formula Calculator solves any second-degree equation of the form ax^2 + bx + c = 0. It handles real and complex roots and shows the discriminant.
How It Works
x = (-b +/- sqrt(b^2 - 4ac)) / 2a. If the discriminant is positive, there are two real roots. If zero, one repeated root. If negative, two complex roots.
Example
x^2 - 5x + 6 = 0: x = (5 +/- sqrt(25-24)) / 2 = (5 +/- 1) / 2 = 3 or 2.
Formula
x = (-b +/- sqrt(b^2 - 4ac)) / 2aReading the Results
Discriminant
Positive = 2 real roots. Zero = 1 repeated root. Negative = 2 complex roots.
Root 1
The first solution using the plus branch of the quadratic formula.
Root 2
The second solution using the minus branch of the quadratic formula.
Frequently Asked Questions
What if the discriminant is negative?
The equation has two complex roots involving the imaginary unit i. The calculator will show complex results.
Can a be zero?
No. If a = 0, the equation becomes linear (bx + c = 0) and has one solution at x = -c/b.
What is the vertex of a parabola?
The vertex is at x = -b/(2a). The calculator shows the roots; you can compute the vertex from the coefficients.