Quadratic Formula Mastery Quiz
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Questions and Answers

What is the quadratic formula for solving the equation $ax^2 + bx + c = 0$?

  • $x = \frac{b \pm \sqrt{b^2 + 4ac}}{2a}
  • $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ (correct)
  • $x = \frac{b \pm \sqrt{b^2 - 4ac}}{2a}$
  • $x = \frac{-b \pm \sqrt{b^2 + 4ac}}{2a}$
  • What is the discriminant of a quadratic equation $ax^2 + bx + c = 0$?

  • $b^2 + 4ac$
  • $b^2 - 4ac$ (correct)
  • $-b^2 - 4ac$
  • $-b^2 + 4ac$
  • What is the solution to the quadratic equation $2x^2 - 5x + 2 = 0$ using the quadratic formula?

  • $x = \frac{5}{2}, x = 2$
  • $x = \frac{1}{2}, x = 2$
  • $x = 2, x = \frac{1}{2}$ (correct)
  • $x = 2, x = -\frac{1}{2}$
  • When does the quadratic formula give imaginary roots for a quadratic equation?

    <p>When the discriminant is negative</p> Signup and view all the answers

    What is the general form of a quadratic equation?

    <p>$ax^2 + bx + c = 0$</p> Signup and view all the answers

    Study Notes

    Quadratic Formula

    • The quadratic formula is: x = (-b ± √(b^2 - 4ac)) / 2a

    Discriminant of a Quadratic Equation

    • The discriminant of a quadratic equation ax^2 + bx + c = 0 is b^2 - 4ac

    Solution to a Quadratic Equation

    • The solution to the quadratic equation 2x^2 - 5x + 2 = 0 using the quadratic formula is: x = (5 ± √(25 - 16)) / 4
    • Simplifying the solution, we get: x = (5 ± √9) / 4, or x = (5 ± 3) / 4

    Imaginary Roots

    • The quadratic formula gives imaginary roots for a quadratic equation when the discriminant (b^2 - 4ac) is negative

    General Form of a Quadratic Equation

    • The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0

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    Description

    Test your skills in solving quadratic equations using the quadratic formula with this intermediate algebra quiz. Practice applying the quadratic formula to find the solutions for various quadratic equations.

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