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Quadratic Equations Flashcards

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

Read the first 6 Quadratic Equations flashcards as text

  1. What is the sum of the roots of x² - 7x + 10 = 0?

    Answer: 7

    By Vieta's formulas, the sum of roots = -b/a = 7/1 = 7.

  2. Solve x² + 2x - 15 = 0 by factoring.

    Answer: x = 3 and x = -5

    Factor as (x + 5)(x - 3) = 0, giving x = 3 and x = -5.

  3. How many real solutions does x² + 1 = 0 have?

    Answer: No real solutions

    x² = -1 has no real solutions because a square cannot be negative.

  4. Which form of a quadratic is easiest for reading the roots directly?

    Answer: Factored form

    Factored form y = a(x - r₁)(x - r₂) directly shows the roots r₁ and r₂.

  5. What is the product of the roots of 2x² - 6x + 4 = 0?

    Answer: 2

    By Vieta's formulas, the product of roots = c/a = 4/2 = 2.

  6. Complete the square: x² + 6x + __ = (x + 3)²

    Answer: 9

    (x + 3)² = x² + 6x + 9, so the missing constant is 9.