Quadratic Equations: The Discriminant
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Questions and Answers

Which of the following statements are true of the discriminant? (Select all that apply)

  • The discriminant is the radicand of the quadratic formula. (correct)
  • The discriminant is $b^2 - 4ac$ in the quadratic formula. (correct)
  • The discriminant is the value under the radical in the quadratic formula. (correct)
  • Use the discriminant to describe the roots of the equation $x^2 - 4x + 4 = 0$. Select all answer options that apply.

  • Imaginary root
  • Real and rational root (correct)
  • Real and irrational root
  • Double root (correct)
  • Use the discriminant to describe the roots of the equation $x^2 - 5x + 7 = 0$. What is the best description?

    Imaginary root

    Use the discriminant to describe the roots of the equation $x^2 - 5x - 4 = 0$. What is the best description?

    <p>Real and irrational root</p> Signup and view all the answers

    Use the discriminant to describe the roots of the equation $16x^2 + 8x + 1 = 0$. Select all answer options that apply.

    <p>Double root</p> Signup and view all the answers

    Use the discriminant to describe the roots of the equation $x^2 + 9x + 14 = 0$. What is the best description?

    <p>Real and rational root</p> Signup and view all the answers

    Use the discriminant to describe the roots of the equation $3x^2 - 10 = 0$. What is the best description?

    <p>Real and irrational root</p> Signup and view all the answers

    Use the discriminant to describe the roots of the equation $2 = x^2 + 5x$. What is the best description?

    <p>Real and irrational root</p> Signup and view all the answers

    Use the discriminant to describe the roots of the equation $2m^2 + 3 = m$. What is the best description?

    <p>Imaginary root</p> Signup and view all the answers

    Use the discriminant to describe the roots of the equation $6x^2 + 13x + 6 = 0$. What is the best description?

    <p>Real and rational root</p> Signup and view all the answers

    Use the discriminant to describe the roots of the equation $2x^2 + 7x + 6 = 0$. What is the best description?

    <p>Real and rational root</p> Signup and view all the answers

    Use the discriminant to describe the roots of the equation $7x^2 + 1 = 5x$. What is the best description?

    <p>Imaginary root</p> Signup and view all the answers

    Use the discriminant to describe the roots of the equation $7x^2 + 3 = 8x$. What is the best description?

    <p>Imaginary root</p> Signup and view all the answers

    Use the discriminant to describe the roots of the equation $3x^2 - 2 + 7x = 0$. What is the best description?

    <p>Real and irrational root</p> Signup and view all the answers

    Use the discriminant to describe the roots of the equation $x^2 - 6x + 9 = 0$. Select all answer options that apply.

    <p>Double root</p> Signup and view all the answers

    Use the discriminant to describe the roots of the equation $x^2 - 6x + 12 = 0$. What is the best description?

    <p>Imaginary root</p> Signup and view all the answers

    Study Notes

    Discriminant Overview

    • The discriminant is calculated using the formula b² - 4ac in a quadratic equation ax² + bx + c = 0.
    • It determines the nature of the roots of a quadratic equation.

    Root Types Based on Discriminant Value

    • A discriminant greater than zero indicates two distinct real and rational roots.
    • A discriminant equal to zero indicates a double root (or one real root).
    • A discriminant less than zero indicates two complex (imaginary) roots.

    Example Equations

    • x² - 4x + 4 = 0: Roots are real and rational, classified as a double root.

    • x² - 5x + 7 = 0: Roots are imaginary.

    • x² - 5x - 4 = 0: Roots are real and irrational.

    • 16x² + 8x + 1 = 0: Roots are real and rational, also classified as a double root.

    • x² + 9x + 14 = 0: Roots are real and rational.

    • 3x² - 10 = 0: Roots are real and irrational.

    • 2 = x² + 5x: Roots are real and irrational.

    • 2m² + 3 = m: Roots are imaginary.

    • 6x² + 13x + 6 = 0: Roots are real and rational.

    • 2x² + 7x + 6 = 0: Roots are real and rational.

    • 7x² + 1 = 5x: Roots are imaginary.

    • 7x² + 3 = 8x: Roots are imaginary.

    • 3x² - 2 + 7x = 0: Roots are real and irrational.

    • x² - 6x + 9 = 0: Roots are real and rational, classified as a double root.

    • x² - 6x + 12 = 0: Roots are imaginary.

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    Description

    Test your knowledge about the discriminant in quadratic equations. This quiz covers its definition, properties, and how to use it to determine the nature of roots in equations. Perfect for students studying algebra and quadratic functions.

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