Quadratic Formula

Everything on this page applies given a quadratic equation in the form \(Ax^2 + Bx + C = 0\), where A, B, and C are constants.

Use

\[x=\frac{-B\pm\sqrt{B^{2}-4AC}}{2A}\]

to find all solutions to the quadratic equation.

Formulas for the Solutions

\(-\frac{B}{A}\) is the sum of the solutions.

\(\frac{C}{A}\) is the product of the solutions.

Discriminant

The discriminant is \(B^{2}-4AC\) (the part under the square root in the quadratic formula), and its value means one of three things:

• Greater than zero: there are 2 real solutions.
• Exactly zero: there is 1 real solution.
• Less than zero: there are no real solutions.

❓ How do I make the math bigger?

Right-click or long press any of the math, then click Math Settings → Scale All Math... Type a number such as 125% or 200%.