Quadratic Equations

A quadratic equation in variable x

A quadratic equation in variable x has the form ax^2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. Any equation that can be simplified to th

The standard form is ax^2 +

The standard form is ax^2 + bx + c = 0, with terms written in descending order of powers of x.

A real number α is

A real number α is a root if substituting x = α makes the equation true, so aα^2 + bα + c = 0.

The quadratic is written as

The quadratic is written as a product of two linear factors. Then each factor is set equal to zero. A common step is to find p and q such that p + q =

The equation is rearranged so

The equation is rearranged so the left side becomes a perfect square. For ax^2 + bx + c = 0, dividing by a and completing the square leads to [x + b/(