Q. Find the value of x in the equation 3x^2 + 12x + 12 = 0.
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Solution
Dividing the entire equation by 3 gives x^2 + 4x + 4 = 0. Factoring gives (x + 2)(x + 2) = 0, so x = -2.
Correct Answer:
B
— -4
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Q. Solve for x: 2x^2 - 8 = 0.
A.
-2 and 2
B.
2 and -2
C.
4 and -4
D.
0 and 4
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Solution
First, add 8 to both sides: 2x^2 = 8. Then divide by 2: x^2 = 4. Taking the square root gives x = ±2.
Correct Answer:
A
— -2 and 2
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Q. What are the roots of the equation 3x^2 + 12x + 12 = 0?
A.
x = -2
B.
x = -4
C.
x = -2, -2
D.
x = 0
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Solution
Using the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a, we find x = (-12 ± √(144 - 144)) / 6 = -2.
Correct Answer:
C
— x = -2, -2
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Q. What is the factored form of the polynomial x^2 - 6x + 9?
A.
(x - 3)(x - 3)
B.
(x + 3)(x + 3)
C.
(x - 9)(x + 1)
D.
(x + 6)(x - 3)
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Solution
The polynomial x^2 - 6x + 9 can be factored as (x - 3)(x - 3) or (x - 3)^2.
Correct Answer:
A
— (x - 3)(x - 3)
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Q. What is the solution set for the equation 3x + 4 = 10?
A.
x = 2
B.
x = 3
C.
x = 4
D.
x = 1
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Solution
To solve 3x + 4 = 10, subtract 4 from both sides: 3x = 6. Then divide by 3: x = 2.
Correct Answer:
A
— x = 2
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Q. What is the solution set for the equation x^2 - 9 = 0?
A.
x = 3, -3
B.
x = 9
C.
x = 0
D.
x = 1, -1
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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 quadratic equation x^2 + 6x + 9 = 0?
A.
x = -3
B.
x = 3
C.
x = 0
D.
x = -6
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Solution
The equation x^2 + 6x + 9 can be factored as (x + 3)(x + 3) = 0. Thus, the solution is x = -3.
Correct Answer:
A
— x = -3
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Q. What is the sum of the roots of the equation x^2 + 6x + 9 = 0?
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Solution
The sum of the roots can be found using -b/a. Here, b = 6 and a = 1, so the sum is -6.
Correct Answer:
A
— -6
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Q. What is the value of x in the equation 5x + 3 = 18?
A.
x = 3
B.
x = 4
C.
x = 5
D.
x = 2
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Solution
To solve 5x + 3 = 18, subtract 3 from both sides: 5x = 15. Then divide by 5: x = 3.
Correct Answer:
B
— x = 4
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Q. What is the vertex of the parabola represented by y = x^2 - 4x + 3?
A.
(2, -1)
B.
(2, 1)
C.
(1, 2)
D.
(3, 0)
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Solution
The vertex can be found using the formula x = -b/(2a). Here, a = 1, b = -4. Thus, x = 2. Plugging x back into the equation gives y = 1. So, the vertex is (2, 1).
Correct Answer:
A
— (2, -1)
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Q. Which of the following inequalities represents the solution to 3x + 2 > 11?
A.
x > 3
B.
x < 3
C.
x > 4
D.
x < 4
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Solution
Subtracting 2 from both sides gives 3x > 9. Dividing by 3 results in x > 3.
Correct Answer:
C
— x > 4
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Q. Which of the following is a factor of x^2 - 9?
A.
(x - 3)
B.
(x + 3)
C.
(x - 3)(x + 3)
D.
(x^2 + 9)
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Solution
x^2 - 9 is a difference of squares and can be factored as (x - 3)(x + 3).
Correct Answer:
C
— (x - 3)(x + 3)
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Q. Which of the following represents the quadratic equation with roots 1 and -3?
A.
x^2 + 2x - 3 = 0
B.
x^2 - 2x - 3 = 0
C.
x^2 + 2x + 3 = 0
D.
x^2 - 4 = 0
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Solution
Using the roots, we can write the equation as (x - 1)(x + 3) = 0, which expands to x^2 + 2x - 3 = 0.
Correct Answer:
A
— x^2 + 2x - 3 = 0
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