Advanced Math / Nonlinear Equations One Variable
Nonlinear Equations in One Variable
Nonlinear equations in one variable can include quadratics, equations with radicals, rational equations, powers, and equations written in factored or transformed forms.
Least you need to know
- A quadratic equation can often be solved by factoring or using structure from its roots.
- Squaring both sides of an equation with radicals can introduce extraneous solutions.
Key notation
- $(x-a)(x-b)=0$ — An equation whose solutions are $x=a$ and $x=b$
Worked example
- Rearrange or factor the equation.
- Check restrictions when radicals or rational expressions are involved.
Common mistakes
- Do not divide by an expression that could be zero without considering that case.
- Check proposed radical-equation solutions.
How to recognize it
- The equation includes powers, roots, rational expressions, or parameters.
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