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The roots of a quadratic equation depend on the values of the coefficients.
The roots of a quadratic equation depend on the values of the coefficients.
True
What are the values of a, b, and c in the equation $x^2 + 6x - 55 = 0$?
What are the values of a, b, and c in the equation $x^2 + 6x - 55 = 0$?
1, 6, -55
What is the sum of the roots of $x^2 + 6x - 55 = 0$?
What is the sum of the roots of $x^2 + 6x - 55 = 0$?
-6
What is the product of the roots of $x^2 + 6x - 55 = 0$?
What is the product of the roots of $x^2 + 6x - 55 = 0$?
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What are the values of a, b, and c for the equation $8x^2 - 2x = 1$?
What are the values of a, b, and c for the equation $8x^2 - 2x = 1$?
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What is the sum of the roots of $8x^2 - 2x = 1$?
What is the sum of the roots of $8x^2 - 2x = 1$?
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What is the product of the roots of $8x^2 - 2x = 1$?
What is the product of the roots of $8x^2 - 2x = 1$?
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Which of the following could be the solution set to $8x^2 - 2x = 1$?
Which of the following could be the solution set to $8x^2 - 2x = 1$?
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What is the sum of the roots of the equation $x^2 + x = 2$?
What is the sum of the roots of the equation $x^2 + x = 2$?
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What is the product of the roots of the equation $x^2 + x = 2$?
What is the product of the roots of the equation $x^2 + x = 2$?
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What is the sum of the roots of the equation $\frac{1}{2}x^2 - \frac{5}{4}x - 3 = 0$?
What is the sum of the roots of the equation $\frac{1}{2}x^2 - \frac{5}{4}x - 3 = 0$?
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What is the product of the roots of the equation $\frac{1}{2}x^2 - \frac{5}{4}x - 3 = 0$?
What is the product of the roots of the equation $\frac{1}{2}x^2 - \frac{5}{4}x - 3 = 0$?
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What is the sum of the roots of the equation $5 - 2m - 3m^2 = 0$?
What is the sum of the roots of the equation $5 - 2m - 3m^2 = 0$?
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What is the product of the roots of the equation $5 - 2m - 3m^2 = 0$?
What is the product of the roots of the equation $5 - 2m - 3m^2 = 0$?
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If the roots of a quadratic equation are $1 \pm \sqrt{5}$, what is the product of the roots?
If the roots of a quadratic equation are $1 \pm \sqrt{5}$, what is the product of the roots?
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Study Notes
Roots of Quadratic Equations
- Roots depend on the coefficients of the quadratic equation.
- For the equation (x^2 + 6x - 55 = 0), the coefficients are (a=1), (b=6), and (c=-55).
Sum and Product of Roots
- The sum of the roots for (x^2 + 6x - 55 = 0) is calculated as (-b/a), resulting in (-6).
- The product of the roots for the same equation is (c/a), which gives (-55).
Coefficients in Different Equations
- For the equation (8x^2 - 2x = 1), the coefficients are (a=8), (b=-2), and (c=-1).
- The sum of the roots for (8x^2 - 2x = 1) equals (1/4).
- The product of the roots for this quadratic is (-1/8).
Solution Set
- A potential solution set for (8x^2 - 2x = 1) includes {-1/4, 1/2}.
Additional Quadratic Equations
- For the equation (x^2 + x = 2):
- The sum of the roots is (-1).
- The product of the roots is (-2).
Specific Equations with Fractions
- In the quadratic equation (\frac{1}{2}x^2 - \frac{5}{4}x - 3 = 0):
- The sum of the roots equals (5/2).
- The product of the roots is (-6).
Roots of Different Variables
- For the equation (5 - 2m - 3m^2 = 0):
- The sum of the roots is (-2/3).
- The product of the roots is (-5/3).
Special Cases of Roots
- If the roots of a quadratic equation are given as (1 ± \sqrt{5}), the product of these roots is (-4).
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Description
This quiz covers the concepts of sum and product of roots in quadratic equations, focusing on specific examples like x² + 6x - 55 = 0. It assesses your understanding of how coefficients determine the roots and how to calculate their sum and product. Test your knowledge with this set of flashcards!
