Quadratic Formula Calculator

Solve quadratic equations of the form ax² + bx + c = 0.

x = [-b ± √(b²-4ac)] / 2a

About this Tool

The Quadratic Formula Calculator solves quadratic equations of the form ax² + bx + c = 0. This is a staple of algebra, and the calculator provides the roots of the equation, whether they are real or complex.

Common Use Cases

Algebra Homework

Quickly find the solutions to quadratic equations for math assignments.

Physics Problems

Solve for variables in physics problems that involve projectile motion or other phenomena modeled by quadratic equations.

Engineering

Find points of interest in engineering problems that can be modeled with quadratic functions, such as the shape of a parabolic antenna.

Pro Tips

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    The Discriminant

    The value inside the square root (b² - 4ac) is called the discriminant. It tells you the nature of the roots: if it's positive, there are two real roots; if it's zero, there is one real root; if it's negative, there are two complex roots.

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    Standard Form

    Make sure your equation is in the standard form ax² + bx + c = 0 before you identify the coefficients a, b, and c.

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    Coefficient 'a'

    The coefficient 'a' cannot be zero. If a=0, the equation is linear, not quadratic.

Frequently Asked Questions