Solve quadratic and absolute value equations, including factoring and reasoning about multiple solutions.
79 original nonlinear equations and systems questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.
What are the solutions to x² + 4x + 3 = 0?
Factoring gives (x + 1)(x + 3) = 0, so x = -1 or x = -3.
What are the solutions to x² + 3x - 54 = 0?
Factoring gives (x + 9)(x - 6) = 0, so x = -9 or x = 6.
What is the sum of the solutions to x² − 8x + 15 = 0?
Factoring gives (x − 3)(x − 5) = 0, so the solutions are 3 and 5, which sum to 8.
What is the solution set of |2x − 4| = 10?
2x − 4 = 10 gives x = 7. 2x − 4 = -10 gives x = -3. So x = -3 or x = 7.
What are the solutions to x² − 5x + 6 = 0?
Factor: (x − 2)(x − 3) = 0, so x = 2 or x = 3.