Equation in quadratic form

Definition

An equation in quadratic form is a polynomial equation that can be rewritten as a quadratic equation by making an appropriate substitution. Typically, it takes the form $a(u)^2 + b(u) + c = 0$ where $u$ is a function of $x$.

5 Must Know Facts For Your Next Test

1. Equations in quadratic form often require substitution to simplify into a standard quadratic equation.
2. The roots of the quadratic form equation can be found using the quadratic formula after substitution.
3. Identifying the correct substitution is key to solving equations in quadratic form.
4. The discriminant ($b^2 - 4ac$) determines the nature of the roots just like in standard quadratics.
5. After finding the solutions for $u$, you must back-substitute to find the solutions in terms of $x$.

Review Questions

• What steps are involved in solving an equation in quadratic form?
• How do you determine the correct substitution for rewriting an equation in quadratic form?
• What role does the discriminant play when solving an equation in quadratic form?

Related terms

Quadratic Equation: A second-degree polynomial equation of the form $ax^2 + bx + c = 0$, where $a \neq 0$.

Substitution Method: A method used to solve equations by replacing one variable with another expression.

Discriminant: In a quadratic equation $ax^2 + bx + c = 0$, it is the value given by $b^2 - 4ac$ which determines the nature and number of roots.