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The Quadratic Formula quiz #1 Flashcards

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The Quadratic Formula quiz #1
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  • What is the quadratic formula and when is it used in chemistry?
    The quadratic formula is x = [-b ± sqrt(b² - 4ac)] / (2a). It is used to solve equations where x is squared, such as in chemical equilibrium problems to find equilibrium concentrations.
  • How do you solve the equation x² – 10x = 24 using the quadratic formula?
    First, rewrite the equation in standard form: x² – 10x – 24 = 0. Identify a = 1, b = -10, c = -24, then substitute into the quadratic formula: x = [10 ± sqrt(100 - 4(1)(-24))]/2.
  • How do you solve the equation 3x² – 12x + 24 = 0 using the quadratic formula?
    Identify a = 3, b = -12, c = 24. Substitute into the quadratic formula: x = [12 ± sqrt(144 - 4(3)(24))]/(2*3).
  • How do you find the solution set for x² – 10 = 30x using the quadratic formula?
    Rewrite as x² – 30x – 10 = 0. Identify a = 1, b = -30, c = -10, then use the quadratic formula: x = [30 ± sqrt(900 - 4(1)(-10))]/2.
  • How do you solve for x in the equation 2x² + 8x = x² – 16 using the quadratic formula?
    First, bring all terms to one side: 2x² + 8x – x² + 16 = 0, which simplifies to x² + 8x + 16 = 0. Use a = 1, b = 8, c = 16 in the quadratic formula: x = [-8 ± sqrt(64 - 64)]/2.
  • How do you solve the equation 2x² – 11 = 87 using the quadratic formula?
    Rewrite as 2x² – 98 = 0. Identify a = 2, b = 0, c = -98, then use the quadratic formula: x = [0 ± sqrt(0 - 4(2)(-98))]/(2*2).
  • How do you find the positive solution to x² + 9x – 22 = 0 using the quadratic formula?
    Identify a = 1, b = 9, c = -22. Substitute into the quadratic formula: x = [-9 ± sqrt(81 - 4(1)(-22))]/2. The positive solution is the value with the plus sign.
  • How do you solve the inequality x² + 4x < 77 using the quadratic formula?
    Rewrite as x² + 4x – 77 < 0. Find the roots using the quadratic formula: x = [-4 ± sqrt(16 + 308)]/2. The solution set is the values of x between the two roots.
  • How can you determine if a quadratic equation has one real solution using the quadratic formula?
    A quadratic equation has one real solution if the discriminant (b² - 4ac) equals zero.
  • How do you find the solution set for x² + 5x – 5 = 0 using the quadratic formula?
    Identify a = 1, b = 5, c = -5. Substitute into the quadratic formula: x = [-5 ± sqrt(25 + 20)]/2.