Questions and Answers
Which of the following statements are true of the discriminant? (Select all that apply)
Use the discriminant to describe the roots of the equation $x^2 - 4x + 4 = 0$. Select all answer options that apply.
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?
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Use the discriminant to describe the roots of the equation $16x^2 + 8x + 1 = 0$. Select all answer options that apply.
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Use the discriminant to describe the roots of the equation $x^2 + 9x + 14 = 0$. What is the best description?
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Use the discriminant to describe the roots of the equation $3x^2 - 10 = 0$. What is the best description?
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Use the discriminant to describe the roots of the equation $2 = x^2 + 5x$. What is the best description?
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Use the discriminant to describe the roots of the equation $2m^2 + 3 = m$. What is the best description?
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Use the discriminant to describe the roots of the equation $6x^2 + 13x + 6 = 0$. What is the best description?
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Use the discriminant to describe the roots of the equation $2x^2 + 7x + 6 = 0$. What is the best description?
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Use the discriminant to describe the roots of the equation $7x^2 + 1 = 5x$. What is the best description?
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Use the discriminant to describe the roots of the equation $7x^2 + 3 = 8x$. What is the best description?
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Use the discriminant to describe the roots of the equation $3x^2 - 2 + 7x = 0$. What is the best description?
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Use the discriminant to describe the roots of the equation $x^2 - 6x + 9 = 0$. Select all answer options that apply.
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Use the discriminant to describe the roots of the equation $x^2 - 6x + 12 = 0$. What is the best description?
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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
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x² - 4x + 4 = 0: Roots are real and rational, classified as a double root.
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x² - 5x + 7 = 0: Roots are imaginary.
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x² - 5x - 4 = 0: Roots are real and irrational.
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16x² + 8x + 1 = 0: Roots are real and rational, also classified as a double root.
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x² + 9x + 14 = 0: Roots are real and rational.
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3x² - 10 = 0: Roots are real and irrational.
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2 = x² + 5x: Roots are real and irrational.
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2m² + 3 = m: Roots are imaginary.
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6x² + 13x + 6 = 0: Roots are real and rational.
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2x² + 7x + 6 = 0: Roots are real and rational.
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7x² + 1 = 5x: Roots are imaginary.
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7x² + 3 = 8x: Roots are imaginary.
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3x² - 2 + 7x = 0: Roots are real and irrational.
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x² - 6x + 9 = 0: Roots are real and rational, classified as a double root.
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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.
