Q. Find the roots of the equation 3x^2 + 6x + 3 = 0.
A.
x = -1
B.
x = -3
C.
x = 1
D.
x = 3
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Solution
This can be simplified to x^2 + 2x + 1 = 0, which factors to (x + 1)(x + 1) = 0. Thus, the root is x = -1.
Correct Answer:
A
— x = -1
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Q. Find the roots of the equation 3x^2 - 12 = 0.
A.
x = 2, -2
B.
x = 4, -4
C.
x = 2, 4
D.
x = -4, 2
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Solution
Add 12 to both sides: 3x^2 = 12. Divide by 3: x^2 = 4. Thus, x = ±2.
Correct Answer:
A
— x = 2, -2
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Q. Find the roots of the quadratic equation 3x^2 + 6x + 3 = 0.
A.
x = -1
B.
x = -3
C.
x = 1
D.
x = 3
Show solution
Solution
Dividing the equation by 3 gives x^2 + 2x + 1 = 0, which factors to (x + 1)(x + 1) = 0. Thus, x = -1.
Correct Answer:
A
— x = -1
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Q. Find the roots of the quadratic equation 4x^2 - 12x + 9 = 0.
A.
x = 1.5
B.
x = 3
C.
x = 0
D.
x = -3
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Solution
This can be factored as (2x - 3)(2x - 3) = 0. Thus, x = 3.
Correct Answer:
B
— x = 3
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Q. Find the value of x in the inequality 3x - 5 < 4.
A.
x < 3
B.
x > 3
C.
x < 1
D.
x > 1
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Solution
Add 5 to both sides: 3x < 9. Divide by 3: x < 3.
Correct Answer:
A
— x < 3
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Q. If 2x + 3 > 7, what is the solution for x?
A.
x > 2
B.
x < 2
C.
x > 3
D.
x < 3
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Solution
Subtract 3 from both sides: 2x > 4. Divide by 2: x > 2.
Correct Answer:
A
— x > 2
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Q. Solve for x in the equation x^2 + 4x + 4 = 0.
A.
x = -2
B.
x = 2
C.
x = 0
D.
x = -4
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Solution
This factors to (x + 2)(x + 2) = 0. Therefore, x = -2.
Correct Answer:
A
— x = -2
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Q. Solve for x: 4x^2 + 8x = 0.
A.
x = 0, -2
B.
x = 2, -2
C.
x = 0, 2
D.
x = -4, 0
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Solution
Factor out 4x: 4x(x + 2) = 0. Thus, x = 0 or x + 2 = 0 gives x = -2.
Correct Answer:
A
— x = 0, -2
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Q. Solve the quadratic equation x^2 + 6x + 9 = 0.
A.
x = -3
B.
x = 3
C.
x = -6
D.
x = 6
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Solution
This can be factored as (x + 3)(x + 3) = 0. Therefore, x + 3 = 0 gives x = -3.
Correct Answer:
A
— x = -3
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Q. What are the solutions to the equation x^2 - 10x + 21 = 0?
A.
x = 3, 7
B.
x = -3, -7
C.
x = 1, 21
D.
x = 0, 10
Show solution
Solution
Factoring gives (x - 3)(x - 7) = 0. Thus, the solutions are x = 3 and x = 7.
Correct Answer:
A
— x = 3, 7
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Q. What are the solutions to the equation x^2 - 4 = 0?
A.
x = 2, -2
B.
x = 4, -4
C.
x = 0, 4
D.
x = 0, -4
Show solution
Solution
Factoring gives (x - 2)(x + 2) = 0. Thus, the solutions are x = 2 and x = -2.
Correct Answer:
A
— x = 2, -2
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Q. What are the solutions to the equation x^2 - 9 = 0?
A.
x = 3, -3
B.
x = 0, 9
C.
x = 1, -1
D.
x = 2, -2
Show solution
Solution
Factoring gives (x - 3)(x + 3) = 0. Thus, the solutions are x = 3 and x = -3.
Correct Answer:
A
— x = 3, -3
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Q. What is the solution to the equation 2x^2 - 4x - 6 = 0 using the quadratic formula?
A.
x = 3
B.
x = -1
C.
x = 2
D.
x = -3
Show solution
Solution
Using the quadratic formula x = (-b ± √(b² - 4ac)) / 2a. Here, a = 2, b = -4, c = -6. Discriminant = (-4)² - 4(2)(-6) = 16 + 48 = 64. Thus, x = (4 ± √64) / 4 = (4 ± 8) / 4. Solutions are x = 3 and x = -1.
Correct Answer:
A
— x = 3
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Q. What is the solution to the equation x^2 + 2x - 8 = 0?
A.
x = 2, -4
B.
x = -2, 4
C.
x = 4, -2
D.
x = -4, 2
Show solution
Solution
Factoring gives (x + 4)(x - 2) = 0. Thus, x = -4 or x = 2.
Correct Answer:
C
— x = 4, -2
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Q. What is the solution to the inequality 2x - 3 < 5?
A.
x < 4
B.
x > 4
C.
x < 1
D.
x > 1
Show solution
Solution
Add 3 to both sides: 2x < 8. Divide by 2: x < 4.
Correct Answer:
A
— x < 4
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