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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. If 3x² − 75 = 0, what are the solutions for x?

    Answer: x = ±5

    3x² = 75 → x² = 25 → x = ±5.

  2. The system y = x² and y = 3x − 2 intersects at two points. What is the larger x-value?

    Answer: x = 2

    x² = 3x − 2 → x² − 3x + 2 = 0 → (x − 1)(x − 2) = 0; larger x = 2.

  3. For what positive value of x does x² − 5x + 4 = 0?

    Answer: x = 1 and x = 4 (both positive)

    (x − 1)(x − 4) = 0; both x = 1 and x = 4 are positive solutions.

  4. A parabola opens downward and has x-intercepts at x = −1 and x = 5. Which equation could model this parabola?

    Answer: y = −(x + 1)(x − 5)

    x-intercepts at −1 and 5 give factors (x + 1)(x − 5); downward opening requires a negative leading coefficient: y = −(x + 1)(x − 5).

  5. The roots of x² − 8x + 15 = 0 are p and q. What is the value of p² + q²?

    Answer: 34

    p + q = 8; pq = 15; p² + q² = (p + q)² − 2pq = 64 − 30 = 34.

  6. What value of m makes mx² − 6x + 1 = 0 have exactly one real solution?

    Answer: m = 9

    One real solution when discriminant = 0: (−6)² − 4m(1) = 0 → 36 = 4m → m = 9.

  7. If x² + 5x = −6, what are the solutions?

    Answer: x = −2 and x = −3

    x² + 5x + 6 = 0 → (x + 2)(x + 3) = 0; x = −2 or x = −3.