10

Set 11: Quadratic Equations (Advanced)

Explanation

Answer: A

Find two numbers whose sum is 20 and whose product is a maximum.

A.

10 and 10

✓ Correct
B.

0 and 20

C.

5 and 15

D.

8 and 12

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Setup: Let the numbers be xx and 20−x20 -x. 2. Product Function: P(x)=x(20−x)=−x2+20xP(x) = x(20-x) = -x^2 + 20 x. 3. Maximize: Vertex x=−20/(2(−1))=10x = -20 / (2(-1)) = 10. 4. Result: The numbers are 10 and 10. Their product is 100. Choice B is incorrect because product is 0. Choice C is incorrect because product is 75. Choice D is incorrect because product is 96.

Key Steps:

•

The correct answer is 10 and 10

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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