Arithmetic and Geometric Progressions

Arithmetic and Geometric Progressions - Problem Set

Q. What is the factored form of the polynomial x^2 + 7x + 10?

Solution

Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Factor as (x + 5)(x + 2).

Correct Answer: A — (x + 5)(x + 2)

Q. What is the product of the roots of the quadratic equation x^2 + 3x + 2 = 0?

Solution

Step 1: Use the formula c/a. Here, c = 2 and a = 1, so the product is 2/1 = 2.

Correct Answer: A — 2

Q. What is the solution to the inequality 2x + 1 > 3?

Solution

Subtract 1 from both sides: 2x > 2. Then divide by 2: x > 1.

Correct Answer: B — x > 1

Q. Which of the following is the solution set for the inequality 2x + 1 ≥ 5?

Solution

Step 1: Subtract 1 from both sides: 2x ≥ 4. Step 2: Divide by 2: x ≥ 2.

Correct Answer: B — x ≥ 2

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