Math Foundations Equations Quadratic Equations

Incomplete Quadratic Equations

Quadratic equations with missing terms (incomplete quadratics) are the simplest forms of quadratic equations where the coefficient B, C, or both are missing. Let's learn how to solve them correctly in each specific case.

Key elements:

Incomplete quadratic equation

Solving such equations

General formulas

Connections:

Statistics:

Term1

Statement3

Important1

Problem7

Article Summary Practice

When you come across a quadratic equation, don't rush to use complex methods right away. It might turn out that the equation is incomplete:

Incomplete quadratic equation

Quadratic equation, in which coefficient B or C or both are zero:

Examples:

\underbrace{10x^2 = 0}_{B = 0 \ \text{and} \ C = 0}

\underbrace{x^2 + x = 0}_{C = 0}

\underbrace{3x^2 - 8 = 0}_{B = 0}

In that case, solving the equation is simple and fast. You can solve it manually or use general formulas:

\overbrace{5x^2 = 0}^{B = 0 \ \text{and} \ C = 0} \\ \boxed{x = 0}

\overbrace{x^2 + 3x = 0}^{C = 0} \\ \boxed{x_1 = 0} \\ \boxed{x_2 = -\frac{3}{1} = -3}

\overbrace{2x^2 - 8 = 0}^{B = 0} \\ x_{1,2} = \pm \sqrt{-\frac{-8}{2}} \\ x_{1,2} = \pm \sqrt{4} \\ \boxed{x_{1,2} = \pm 2}

Do not memorize general formulas!

It may seem that since we derived general formulas, they must be memorized. This is not true. Do not learn them. Most people don't even remember them. The most important thing is — to be able to quickly notice that the equation is incomplete (consists of one or two terms), which means it is solved quickly and simply!