Quadratic Equations

A quadratic equation is any expression of the form:

ax2 + bx + c = 0,    a ≠ 0.

Solving Quadratic Equations

To solve quadratic equations use the following formula:

Quadratic Formula

Quadratic Equation

Quadratic Operations

Quadratic Equation

Quadratic Operations

If a<0, multiply two members by (−1).

Quadratic Equation

Quadratic Operations

Quadratic Equation

Quadratic Operations

Incomplete Quadratic Equations

A quadratic equation is incomplete if any of its coefficients: b or c, or both, are zero.

Solving Incomplete Quadratic Equations

ax2 = 0

The solution is x = 0.

Quadratic Equation

Quadratic Equation

ax2 + bx = 0

Remove the common factor, x:

Quadratic Equation

The 1st factor equals 0.

Quadratic Solution

A solution is always x = 0.

The other solution was obtained by solving the linear equation resulting from equating the 2nd factor to zero.

Quadratic Solution

Quadratic Equation

Quadratic Operations

Quadratic Solution

Quadratic Solution

Quadratic Equation

Quadratic Operations

Quadratic Operations

Quadratic Solution

ax2 + c = 0

Quadratic Operations

Quadratic Equation

Quadratic Operations

Quadratic Equation

Quadratic Solution