8

Set 11: Quadratic Equations (Intermediate)

Explanation

Answer: A

The product of two consecutive positive even integers is 168. Find the integers.

A.

12 and 14

✓ Correct
B.

10 and 12

C.

14 and 16

D.

8 and 10

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Setup: Let integers be xx and x+2x+2. 2. Equation: x(x+2)=168x2+2x168=0x(x+2) = 168 \Rightarrow x^2 + 2 x - 168 = 0. 3. Factor: (x+14)(x12)=0(x + 14)(x - 12) = 0. 4. Result: x=12x = 12 (since positive). Next integer is 14. Choice B is incorrect because product is 120. Choice C is incorrect because product is 224. Choice D is incorrect because product is 80.

Key Steps:

The correct answer is 12 and 14

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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