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Zero in Equations: Exploring Its Role in Solving Linear and Quadratic Equations

Description: This quiz will test your understanding of the role of zero in solving linear and quadratic equations. You will be presented with various equations and asked to find the value of the variable that makes the equation true.
Number of Questions: 15
Created by:
Tags: zero linear equations quadratic equations algebra
Attempted 0/15 Correct 0 Score 0

Solve the linear equation 3x + 5 = 0.

  1. x = -5/3

  2. x = 5/3

  3. x = 0

  4. x = 1


Correct Option: A
Explanation:

To solve the equation 3x + 5 = 0, we need to isolate the variable x on one side of the equation. We can do this by subtracting 5 from both sides of the equation, which gives us 3x = -5. Then, we can divide both sides of the equation by 3, which gives us x = -5/3.

Solve the quadratic equation x^2 + 4x + 3 = 0.

  1. x = -1, -3

  2. x = 1, -3

  3. x = -1, 3

  4. x = 1, 3


Correct Option: A
Explanation:

To solve the quadratic equation x^2 + 4x + 3 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 1, b = 4, and c = 3. Plugging these values into the formula, we get x = (-4 ± √(4^2 - 4(1)(3))) / 2(1). Simplifying this expression, we get x = (-4 ± √(16 - 12)) / 2. Further simplifying, we get x = (-4 ± √4) / 2. Finally, we get x = (-4 ± 2) / 2. This gives us two solutions: x = -1 and x = -3.

Solve the linear equation 2x - 7 = 1.

  1. x = 4

  2. x = 5

  3. x = 6

  4. x = 7


Correct Option: A
Explanation:

To solve the equation 2x - 7 = 1, we need to isolate the variable x on one side of the equation. We can do this by adding 7 to both sides of the equation, which gives us 2x = 8. Then, we can divide both sides of the equation by 2, which gives us x = 4.

Solve the quadratic equation x^2 - 5x + 6 = 0.

  1. x = 2, 3

  2. x = -2, -3

  3. x = 2, -3

  4. x = -2, 3


Correct Option: A
Explanation:

To solve the quadratic equation x^2 - 5x + 6 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 1, b = -5, and c = 6. Plugging these values into the formula, we get x = (-(-5) ± √((-5)^2 - 4(1)(6))) / 2(1). Simplifying this expression, we get x = (5 ± √(25 - 24)) / 2. Further simplifying, we get x = (5 ± √1) / 2. Finally, we get x = (5 ± 1) / 2. This gives us two solutions: x = 2 and x = 3.

Solve the linear equation 4x + 2 = 10.

  1. x = 2

  2. x = 3

  3. x = 4

  4. x = 5


Correct Option: A
Explanation:

To solve the equation 4x + 2 = 10, we need to isolate the variable x on one side of the equation. We can do this by subtracting 2 from both sides of the equation, which gives us 4x = 8. Then, we can divide both sides of the equation by 4, which gives us x = 2.

Solve the quadratic equation x^2 + 2x - 3 = 0.

  1. x = 1, -3

  2. x = -1, 3

  3. x = 1, 3

  4. x = -1, -3


Correct Option: A
Explanation:

To solve the quadratic equation x^2 + 2x - 3 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 1, b = 2, and c = -3. Plugging these values into the formula, we get x = (-2 ± √(2^2 - 4(1)(-3))) / 2(1). Simplifying this expression, we get x = (-2 ± √(4 + 12)) / 2. Further simplifying, we get x = (-2 ± √16) / 2. Finally, we get x = (-2 ± 4) / 2. This gives us two solutions: x = 1 and x = -3.

Solve the linear equation 5x - 3 = 7.

  1. x = 2

  2. x = 3

  3. x = 4

  4. x = 5


Correct Option: A
Explanation:

To solve the equation 5x - 3 = 7, we need to isolate the variable x on one side of the equation. We can do this by adding 3 to both sides of the equation, which gives us 5x = 10. Then, we can divide both sides of the equation by 5, which gives us x = 2.

Solve the quadratic equation x^2 - 4x + 4 = 0.

  1. x = 2, 2

  2. x = -2, 2

  3. x = 2, -2

  4. x = -2, -2


Correct Option: A
Explanation:

To solve the quadratic equation x^2 - 4x + 4 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 1, b = -4, and c = 4. Plugging these values into the formula, we get x = (-(-4) ± √((-4)^2 - 4(1)(4))) / 2(1). Simplifying this expression, we get x = (4 ± √(16 - 16)) / 2. Further simplifying, we get x = (4 ± √0) / 2. Finally, we get x = (4 ± 0) / 2. This gives us two solutions: x = 2 and x = 2.

Solve the linear equation 6x + 1 = 13.

  1. x = 2

  2. x = 3

  3. x = 4

  4. x = 5


Correct Option: A
Explanation:

To solve the equation 6x + 1 = 13, we need to isolate the variable x on one side of the equation. We can do this by subtracting 1 from both sides of the equation, which gives us 6x = 12. Then, we can divide both sides of the equation by 6, which gives us x = 2.

Solve the quadratic equation x^2 + 6x + 9 = 0.

  1. x = -3, -3

  2. x = 3, 3

  3. x = -3, 3

  4. x = 3, -3


Correct Option: A
Explanation:

To solve the quadratic equation x^2 + 6x + 9 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 1, b = 6, and c = 9. Plugging these values into the formula, we get x = (-6 ± √(6^2 - 4(1)(9))) / 2(1). Simplifying this expression, we get x = (-6 ± √(36 - 36)) / 2. Further simplifying, we get x = (-6 ± √0) / 2. Finally, we get x = (-6 ± 0) / 2. This gives us two solutions: x = -3 and x = -3.

Solve the linear equation 7x - 4 = 10.

  1. x = 2

  2. x = 3

  3. x = 4

  4. x = 5


Correct Option: A
Explanation:

To solve the equation 7x - 4 = 10, we need to isolate the variable x on one side of the equation. We can do this by adding 4 to both sides of the equation, which gives us 7x = 14. Then, we can divide both sides of the equation by 7, which gives us x = 2.

Solve the quadratic equation x^2 - 2x - 3 = 0.

  1. x = 1, -3

  2. x = -1, 3

  3. x = 1, 3

  4. x = -1, -3


Correct Option: A
Explanation:

To solve the quadratic equation x^2 - 2x - 3 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 1, b = -2, and c = -3. Plugging these values into the formula, we get x = (-(-2) ± √((-2)^2 - 4(1)(-3))) / 2(1). Simplifying this expression, we get x = (2 ± √(4 + 12)) / 2. Further simplifying, we get x = (2 ± √16) / 2. Finally, we get x = (2 ± 4) / 2. This gives us two solutions: x = 1 and x = -3.

Solve the linear equation 8x + 5 = 21.

  1. x = 2

  2. x = 3

  3. x = 4

  4. x = 5


Correct Option: A
Explanation:

To solve the equation 8x + 5 = 21, we need to isolate the variable x on one side of the equation. We can do this by subtracting 5 from both sides of the equation, which gives us 8x = 16. Then, we can divide both sides of the equation by 8, which gives us x = 2.

Solve the quadratic equation x^2 + 4x + 2 = 0.

  1. x = -2, -1

  2. x = 2, 1

  3. x = -2, 1

  4. x = 2, -1


Correct Option: A
Explanation:

To solve the quadratic equation x^2 + 4x + 2 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 1, b = 4, and c = 2. Plugging these values into the formula, we get x = (-4 ± √(4^2 - 4(1)(2))) / 2(1). Simplifying this expression, we get x = (-4 ± √(16 - 8)) / 2. Further simplifying, we get x = (-4 ± √8) / 2. Finally, we get x = (-4 ± 2√2) / 2. This gives us two solutions: x = -2 - √2 and x = -2 + √2.

Solve the linear equation 9x - 6 = 15.

  1. x = 2

  2. x = 3

  3. x = 4

  4. x = 5


Correct Option: B
Explanation:

To solve the equation 9x - 6 = 15, we need to isolate the variable x on one side of the equation. We can do this by adding 6 to both sides of the equation, which gives us 9x = 21. Then, we can divide both sides of the equation by 9, which gives us x = 3.

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