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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. What are the solutions to x² − 5x + 6 = 0?

    Answer: x = 2 and x = 3

    Factor as (x−2)(x−3) = 0, giving x = 2 and x = 3.

  2. The quadratic equation x² − 4x + k = 0 has exactly one real solution. What is the value of k?

    Answer: 4

    For exactly one solution the discriminant = 0: (−4)² − 4(1)(k) = 0 → 16 = 4k → k = 4.

  3. Which of the following are both solutions to 2x² + 3x − 2 = 0?

    Answer: x = 1/2 and x = −2

    Factor: (2x−1)(x+2) = 0 → x = 1/2 or x = −2.

  4. How many real solutions does the equation x² + 6x + 10 = 0 have?

    Answer: None

    Discriminant = 6² − 4(1)(10) = 36 − 40 = −4 < 0, so no real solutions exist.

  5. What is the vertex of the parabola y = x² − 8x + 15?

    Answer: (4, −1)

    x-vertex = −(−8)/(2·1) = 4; y = 16 − 32 + 15 = −1; vertex = (4, −1).

  6. Solve for x: x² = 49

    Answer: x = 7 or x = −7

    Taking the square root of both sides gives x = ±7.

  7. The parabola y = x² + bx + c passes through (0, 5) and (5, 0). What is the value of b?

    Answer: −6

    From (0,5): c = 5. From (5,0): 25 + 5b + 5 = 0 → 5b = −30 → b = −6.