Free Quadratic Formula Calculator - Solve ax² + bx + c = 0
Solve any quadratic equation using the quadratic formula. Best free quadratic calculator 2025 - find both roots with step-by-step solution.
Quick Answer
The quadratic formula solves ax² + bx + c = 0: x = (-b ± √(b²-4ac)) / 2a. The discriminant (b²-4ac) determines solution type: >0 = two real roots, =0 = one repeated root, <0 = complex roots. Example: x² - 5x + 6 = 0 gives x = 2 or x = 3. Calculate at practicalwebtools.com.
Key Facts about Quadratic Formula Calculator:
- Quadratic formula: x = (-b ± √(b²-4ac)) / 2a
- Discriminant (b²-4ac) > 0: two distinct real roots
- Discriminant = 0: one repeated real root
- Discriminant < 0: two complex conjugate roots
- Standard form: ax² + bx + c = 0 (a ≠ 0)
- Sum of roots = -b/a, Product of roots = c/a
- Vertex form: a(x-h)² + k, where h = -b/2a
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How to Quadratic Formula Calculator in 3 Easy Steps
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Frequently Asked Questions
Everything you need to know about our quadratic formula calculator
What is the quadratic formula?
x = (-b ± √(b²-4ac)) / 2a - solves ax² + bx + c = 0.
x = (-b ± √(b²-4ac)) / 2a. It solves any quadratic equation ax² + bx + c = 0 by finding the values of x that make the equation true.
What is the discriminant?
b²-4ac: >0 = 2 real, =0 = 1 repeated, <0 = complex roots.
The discriminant is b²-4ac. If >0: two real roots. If =0: one repeated root. If <0: two complex roots. It tells you the nature of solutions.
How do I identify a, b, c?
a = x² coefficient, b = x coefficient, c = constant.
In ax² + bx + c = 0: a is the x² coefficient, b is the x coefficient, c is the constant. Example: 2x² - 5x + 3 = 0 has a=2, b=-5, c=3.
What if the discriminant is negative?
Complex roots involving i = √-1.
Negative discriminant means complex roots with imaginary parts (involving √-1 = i). The roots will be in form (p + qi) and (p - qi).
Still have questions? Try the tool yourself!
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