Q. Find the roots of the equation x^2 + 2x - 8 = 0.
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A.
x = 2, -4
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B.
x = -2, 4
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C.
x = 4, -2
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D.
x = -4, 2
Solution
Factoring gives (x + 4)(x - 2) = 0. Thus, the roots are x = 4 and x = -2.
Correct Answer:
C
— x = 4, -2
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Q. Find the roots of the quadratic equation 3x^2 - 12x = 0.
-
A.
x = 0, 4
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B.
x = 3, 4
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C.
x = 0, 3
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D.
x = 1, 2
Solution
Factoring gives 3x(x - 4) = 0. Thus, x = 0 and x = 4.
Correct Answer:
A
— x = 0, 4
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Q. If 2x + 3 > 7, what is the solution set for x?
-
A.
x > 2
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B.
x < 2
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C.
x > 3
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D.
x < 3
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 5x^2 + 10x = 0.
-
A.
x = 0, -2
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B.
x = 2, -2
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C.
x = 0, 2
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D.
x = -5, 5
Solution
Factoring gives 5x(x + 2) = 0. Thus, x = 0 or x + 2 = 0, giving x = -2.
Correct Answer:
A
— x = 0, -2
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Q. Solve for x in the equation x^2 - 4 = 0.
-
A.
x = 2, -2
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B.
x = 4, -4
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C.
x = 0
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D.
x = 1, -1
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. Solve for x: 4x^2 + 8x + 4 = 0.
-
A.
x = -1
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B.
x = -2
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C.
x = 1
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D.
x = 2
Solution
Factoring gives 4(x^2 + 2x + 1) = 0, or 4(x + 1)(x + 1) = 0. Thus, x = -1.
Correct Answer:
B
— x = -2
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Q. Solve the quadratic equation 3x^2 + 12x + 12 = 0.
-
A.
x = -2
-
B.
x = -4
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C.
x = 0
-
D.
x = -6
Solution
Dividing the entire equation by 3 gives x^2 + 4x + 4 = 0, which factors to (x + 2)(x + 2) = 0. Thus, x = -2.
Correct Answer:
B
— x = -4
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Q. What are the roots of the polynomial equation x^2 - 5x + 6 = 0?
-
A.
x = 2, 3
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B.
x = -2, -3
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C.
x = 1, 6
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D.
x = 0, 5
Solution
Factoring gives (x - 2)(x - 3) = 0. Thus, the roots are x = 2 and x = 3.
Correct Answer:
A
— x = 2, 3
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Q. What is the solution to the equation 4x^2 + 8x + 4 = 0?
-
A.
x = -1
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B.
x = -2
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C.
x = 1
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D.
x = 0
Solution
This can be factored as 4(x^2 + 2x + 1) = 0, which simplifies to 4(x + 1)(x + 1) = 0. Thus, x = -1.
Correct Answer:
B
— x = -2
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Q. What is the solution to the equation 5x^2 - 20 = 0?
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A.
x = 2
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B.
x = -2
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C.
x = 4
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D.
x = -4
Solution
First, add 20 to both sides: 5x^2 = 20. Then divide by 5: x^2 = 4. Taking the square root gives x = 4 and x = -4.
Correct Answer:
C
— x = 4
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Q. What is the solution to the equation x^2 - 7x + 10 = 0?
-
A.
x = 5, 2
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B.
x = 3, 4
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C.
x = 1, 10
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D.
x = 0, 7
Solution
Factoring gives (x - 5)(x - 2) = 0. Thus, x = 5 and x = 2.
Correct Answer:
A
— x = 5, 2
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