Quadratic Equation Calculator
Quadratic formula calculator
Solve ax² + bx + c = 0 with root classification, step-by-step explanation, and copyable LaTeX code.
Solved roots
x1 = 2, x2 = 1
Discriminant: 1. Vertex: (1.5, -0.25). Two distinct real roots.
Two real roots
x = (-b ± √(b² - 4ac)) / (2a)
Root type
Two real roots
Discriminant
1
Axis of symmetry
1.5
Leading coefficient
1
Formula
x = (-b ± √(b² - 4ac)) / (2a)
Use “Copy LaTeX code” if you need equation markup for notes, LMS, or docs.
Step-by-step derivation
- Step 1: Compute discriminant -> Δ = 1.
- Step 2: Since Δ > 0, roots are real and distinct.
- Step 3: Substitute into quadratic formula -> x1 = 2, x2 = 1.
Flow
- Enter coefficients a, b, and c.
- Review roots and discriminant class.
- Copy results or formula output for reports and assignments.
Example
Worked example: x^2 - 5x + 6 = 0
- 1 a = 1, b = -5, c = 6
- 2 Delta = b^2 - 4ac = 25 - 24 = 1
- 3 x = (5 ± 1)/2 => x1 = 3, x2 = 2
Roots are x = 2 and x = 3.
How
- Enter coefficients a, b, and c.
- Review roots and discriminant class.
- Copy results or formula output for reports and assignments.
Avoid
- Entering a = 0, which makes the equation linear rather than quadratic.
- Forgetting minus sign on b in the quadratic formula.
- Assuming negative discriminant means no solution instead of complex roots.
Checks
Best fit
Quadratic Equation Calculator is built for solve quadratic equations ax^2 + bx + c = 0 with real/complex root classification and steps. If Quadratic Equation Calculator does not match the input scope, compare the answer with a second method.
Input check
Match the entered values to this rule before copying the answer: x = (-b ± sqrt(b^2 - 4ac)) / (2a).
Sanity check
For Quadratic Equation Calculator, use the worked example as a quick benchmark: Roots are x = 2 and x = 3. If the quadratic equation calculator answer is far away, check whether an input, unit, or mode changed.
Before copying
Review this common issue first: entering a = 0, which makes the equation linear rather than quadratic.
FAQ
What does the discriminant tell me?
It determines whether roots are distinct real, repeated real, or complex.
Can this solve complex roots?
Yes, it returns conjugate complex roots when discriminant is negative.
Why is coefficient a required?
Without non-zero a, the equation is not quadratic.
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