iCoachMath.com: Examples on The Sum and Product of Solutions - Quadratic Equations and Functions

Curriculum: Arkansas Math Framework Click to change Curriculum

Topic: Quadratic Equations and Functions Click to change Topic

Lesson: The Sum and Product of Solutions Click to change Lesson

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c Find the sum and product of the solutions to the equation.
x² + 8x - 5 = 0
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c Find the sum and product of the solutions to the equation 2m² + 10m + 7 = 0.
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c Find the sum and product of the solutions to the equation 2a² + 11a = - 19.
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c Find the sum and product of the solutions to the equation 7m² - 14m = 0.
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c Find the sum and product of the solutions to the equation 11a² = 47 - 9a. c

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c Choose a quadratic equation that has the solutions 11 and 3.
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c Identify a quadratic equation that has 310 and 109 as the solutions.
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c Choose a quadratic equation that has 187and - 1118as the solutions. c

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c Identify a quadratic equation with solutions 5 and - 8. c

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c Choose a quadratic equation having 9 + 4i and 9 - 4i as the solutions.
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c Choose a quadratic equation whose solutions are (10+7)14 and (10-7)14. c

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c Choose a quadratic equation that has the solutions as (- 3 + 67)11 and (- 3 - 67)11. c

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c The sum of two numbers is 21 and their product is 108. Choose the equation in x and then find the numbers.
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c Which of the following quadratic equations has solutions (4 + 12i)8 and (4 - 12i)8? c

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c Choose a quadratic equation that has the given solutions.
(- 11 + 6i)5 and (- 11 - 6i)5
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c The sum of two numbers is 5712 and their product is 3. Choose the appropriate equation in x and then find the numbers.
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c The sum of two numbers is - 22 and their product is 114. Identify the equation in x and then find the numbers. c

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c The sum of two numbers is 32 and their product is 337. Choose the equation and then find those numbers.
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c Choose a quadratic equation that has one solution as - 6 + 9i5.
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c Choose a quadratic equation whose solutions are (10 + i)6 and (10 - i)6.
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c Choose a quadratic equation that has the solutions 8m + 13n and 8m - 13n. c

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c Choose a quadratic equation that has (- 7a + 8b)15 and (- 7a - 8b)15 as solutions. c

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c Which quadratic equation that has the given solutions (2 + i3)5 and (2 - i3)5?
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c Choose a quadratic equation that has the given solutions.
(- 3 + i7)10 and (- 3 - i7)10 c

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c The sum of two numbers is 4112 and their product is 2. Choose the appropriate equation in x and then find the numbers.
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c Find the sum and product of the solutions to the equation.
x² + 11x - 7 = 0
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c Find the sum and product of the solutions to the equation 9m² + 14m + 12 = 0.
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c Find the sum and product of the solutions to the equation 4a² + 13a = - 25.
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c Find the sum and product of the solutions to the equation 8m² - 12m = 0.
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c Find the sum and product of the solutions to the equation 9a² = 32 - 4a. c

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c Choose a quadratic equation that has the solutions 11 and 9.
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c Identify a quadratic equation that has 23 and 32 as the solutions.
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c Choose a quadratic equation that has 75and - 27as the solutions. c

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c Identify a quadratic equation with solutions 4 and - 12. c

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c Choose a quadratic equation that has 5 + 2 and 5 - 2 as solutions. c

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c Choose a quadratic equation having 7 + 5i and 7 - 5i as the solutions.
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c Choose a quadratic equation whose solutions are (6+3)11 and (6-3)11. c

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c Choose a quadratic equation that has the solutions as (- 3 + 72)10 and (- 3 - 72)10. c

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c The sum of two numbers is 23 and their product is 120. Choose the equation in x and then find the numbers.
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c The sum of two numbers is - 18 and their product is 74. Identify the equation in x and then find the numbers. c

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c The sum of two numbers is 26 and their product is 250. Choose the equation and then find those numbers.
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c Choose a quadratic equation that has the solutions 5m + 7n and 5m - 7n. c

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c Choose a quadratic equation that has (- 5a + 6b)11 and (- 5a - 6b)11 as solutions. c

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c Choose a quadratic equation that has one solution as - 9 + 12i2.
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c Choose a quadratic equation whose solutions are (11 + i)7 and (11 - i)7.
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c Which of the following quadratic equations has solutions (2 + 8i)6 and (2 - 8i)6? c

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c Choose a quadratic equation that has the given solutions.
(- 13 + 10i)3 and (- 13 - 10i)3
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c Which quadratic equation that has the given solutions (4 + i3)8 and (4 - i3)8?
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c Choose a quadratic equation that has the given solutions.
(- 2 + i3)5 and (- 2 - i3)5 c

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c For two different, real solutions (x₁ and b₂) of a quadratic equation, find the condition for the sum and product of these solutions to be equal.
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c The solutions of the quadratic equation x² + px + q = 0 are l and m. Write a quadratic equation that has l2 and m2 as the solutions.
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c The solutions of the quadratic equation x² + px + q = 0 are l and m. Write a quadratic equation that has 1l and 1m as the solutions.
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c The solutions of the quadratic equation x² + px + q = 0 are l and m. Write a quadratic equation that has -l and -m as the solutions.
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c The solutions of the quadratic equation x² + px + q = 0 are l and m. Write a quadratic equation that has l + 2 and m + 2 as the solutions.
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c If the roots of a quadratic equation are 1 and 73, determine the equation of the axis of symmetry.
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c For what value of K, the quadratic equation 2Kx² - 8x + (3K - 2) = 0 has one root as the reciprocal of the other.
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c Find the quadratic equation whose sum of roots is 5 and sum of squares of roots is 37.
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c Find the value of K so that the sum of the roots is equal to the product of the roots of the equation Kx² + 75x + 25K = 0 c

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c The roots of the quadratic equation x² - px + q = 0 are l, m. Find lm+ml in terms of p and q.
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c The solutions of the quadratic equation x² - px + q = 0 are equal in magnitude but opposite in sign. Which of the following is true? c

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c Which quadratic equation has 3 + 2 and 3 - 2 as its solutions? c

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c The solutions of the quadratic equation x² + px + q = 0 are l and m. Write a quadratic equation that has l - 2 and m - 2 as the solutions.
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c For two different, real solutions (x₁ and y₂) of a quadratic equation, find the condition for the sum and product of these solutions to be equal.
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