Find the roots of a quadratic equation in the form ax² + bx + c = 0. Visualize the graph and calculate the vertex, discriminant, and solutions.
For a quadratic equation ax² + bx + c = 0:
x = (-b ± √(b² - 4ac)) / (2a)The term b² - 4ac is called the discriminant (Δ):
Calculate to see the solutions.
Calculate to see function properties.
Find answers to common questions about Online Calculator.
A Quadratic Equation Calculator is an online tool that helps solve quadratic equations of the form ax² + bx + c = 0 by finding the roots using the quadratic formula.
The calculator uses the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. It calculates the discriminant (b² - 4ac) to determine the nature of the roots.
The discriminant Δ = b² - 4ac determines the type of roots:
Δ > 0, there are two distinct real roots.Δ = 0, there is one repeated real root.Δ < 0, the roots are complex (imaginary).Yes, the calculator supports both decimal and fraction values for a, b, and c.
If a = 0, the equation is not quadratic but linear (bx + c = 0). The calculator will either solve it as a linear equation or show an error.
Yes, if the discriminant is negative, the calculator provides complex roots in the form x = p ± qi.
Yes! Quadratic equations are widely used in physics (e.g., projectile motion), engineering, and economics, making this tool useful in multiple fields.
Some versions of the calculator include step-by-step explanations for solving quadratic equations, including calculations for the discriminant and roots.
By default, the calculator provides results with a certain decimal precision. Some versions allow users to customize the decimal places.
If you enter non-numeric values, the calculator will display an error or prompt you to enter valid numbers.
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