Quadratic Equation Solver
Find the roots of a quadratic equation (ax² + bx + c = 0).
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Solve Quadratic Equations with the Quadratic Formula
Our Quadratic Equation Solver instantly finds the roots (real or complex) of any equation in the form ax² + bx + c = 0.
What is a Quadratic Equation?
A quadratic equation is a fundamental algebraic equation of the second degree, meaning it contains a variable raised to the power of 2. It is typically written in the standard form ax² + bx + c = 0, where 'a', 'b', and 'c' are coefficients and 'a' is not zero. Solving a quadratic equation means finding the values of 'x' (called the roots) that make the equation true.
How It Works: The Quadratic Formula
The calculator uses the well-known quadratic formula to solve for 'x':
x = [-b ± √(b² - 4ac)] / 2a
By plugging in the coefficients 'a', 'b', and 'c' from your equation, the calculator finds the roots, whether they are two real numbers, one real number, or two complex numbers.
Frequently Asked Questions
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation in a single variable x with the form ax² + bx + c = 0, where a ≠ 0. The solutions to this equation are called its roots.
How do you solve a quadratic equation?
A quadratic equation can be solved using the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a. The value inside the square root, b² - 4ac, is called the discriminant. It determines the nature of the roots (real or complex).
What does the discriminant tell you?
The discriminant (b² - 4ac) tells you the number and type of solutions. If it's positive, there are two distinct real roots. If it's zero, there is exactly one real root. If it's negative, there are two distinct complex roots (conjugate pairs).
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