Q. What is the solution to the equation x^2 + 6x + 9 = 0?
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A.
x = -3
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B.
x = 3
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C.
x = 0
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D.
x = -6
Solution
Factor the equation: (x + 3)(x + 3) = 0. Thus, x = -3.
Correct Answer:
A
— x = -3
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Q. What is the solution to the inequality 2x + 5 ≥ 3?
-
A.
x ≥ -1
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B.
x ≤ -1
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C.
x ≥ 1
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D.
x ≤ 1
Solution
Subtract 5 from both sides: 2x ≥ -2. Then divide by 2: x ≥ -1.
Correct Answer:
A
— x ≥ -1
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Q. What is the sum of the roots of the quadratic equation x^2 + 6x + 9 = 0?
Solution
Step 1: Use the formula -b/a. Here, b = 6 and a = 1. Step 2: The sum of the roots is -6/1 = -6.
Correct Answer:
A
— -6
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Q. What is the value of x in the equation 4x^2 - 16 = 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
Step 1: Add 16 to both sides: 4x^2 = 16. Step 2: Divide by 4: x^2 = 4. Step 3: Take the square root: x = 2 or x = -2.
Correct Answer:
A
— x = 2
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Q. Which expression represents the expansion of (x + 2)^2?
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A.
x^2 + 4
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B.
x^2 + 4x + 4
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C.
x^2 + 2x + 2
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D.
x^2 + 2x + 4
Solution
Use the formula (a + b)^2 = a^2 + 2ab + b^2: (x + 2)^2 = x^2 + 4x + 4.
Correct Answer:
B
— x^2 + 4x + 4
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Q. Which of the following represents the binomial expansion of (x + 2)^2?
-
A.
x^2 + 4
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B.
x^2 + 4x + 4
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C.
x^2 + 2x + 2
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D.
x^2 + 2
Solution
Step 1: Use the formula (a + b)^2 = a^2 + 2ab + b^2. Step 2: Here, a = x and b = 2. Step 3: The expansion is x^2 + 2(2)x + 2^2 = x^2 + 4x + 4.
Correct Answer:
B
— x^2 + 4x + 4
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