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Nonlinear Equations and Systems Flashcards

7 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 Nonlinear Equations and Systems flashcards as text

  1. Which of the following is equivalent to x² − 16?

    Answer: (x − 4)(x + 4)

    x² − 16 is a difference of squares: (x−4)(x+4).

  2. What is the positive solution of 3x² − 27 = 0?

    Answer: x = 3

    3x² = 27 → x² = 9 → x = ±3; the positive solution is x = 3.

  3. If (x − 3)² = 25, what are the possible values of x?

    Answer: x = 8 or x = −2

    x − 3 = ±5 → x = 8 or x = −2.

  4. Which quadratic has roots at x = −1 and x = 5?

    Answer: x² − 4x − 5

    Using factor form: (x+1)(x−5) = x² − 4x − 5.

  5. How many real solutions does x² + 4 = 0 have?

    Answer: None

    x² = −4 has no real solutions since a square cannot be negative.

  6. The product of two consecutive even integers is 48. Which equation models this situation?

    Answer: n² + 2n − 48 = 0

    Let the smaller even integer be n; n(n+2) = 48 → n² + 2n − 48 = 0.

  7. The graph of y = x² − 2x − 8 crosses the x-axis at two points. What is the distance between these x-intercepts?

    Answer: 6

    Factor: (x−4)(x+2) = 0 → x = 4 or x = −2; distance = |4 − (−2)| = 6.