SAT Nonlinear Equations and Systems study notes

Nonlinear equations can have two roots, one root, or a root that appears only because of an algebraic move. Factoring uses the zero-product rule; squaring a radical equation needs a final check because squaring loses sign information.

Worked example

Solve √(3x + 16) = x + 2.

Squaring gives x² + x − 12 = 0, so candidates are 3 and −4. In the original equation, x = 3 gives 5 = 5; x = −4 gives 2 = −2, so −4 is extraneous.

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