Quadratic Formula

In elementary algebra, the quadratic formula is a closed-form expression that gives the solutions of a quadratic equation of the standard form a x squared plus b x plus c equals zero, where a, b and c are known coefficients. It states that x equals negative b, plus or minus the square root of b squared minus 4ac, all divided by 2a, and yields up to two solutions. The quantity under the square root, b squared minus 4ac, is called the discriminant, and its sign tells the nature of the solutions: two distinct real roots when it is positive, one repeated real root when it is zero, and two complex conjugate roots when it is negative. Geometrically, the solutions are the points where the parabola described by the equation crosses the x axis.