8

Set 11: Quadratic Equations

Explanation

Answer: A

Revenue is given by R(x)=(100−x)(20+x)R(x) = (100 - x)(20 + x). Find the x-intercepts of this function.

A.

x=100,−20x = 100, -20

✓ Correct
B.

x=−100,20x = -100, 20

C.

x=100,20x = 100, 20

D.

x=−100,−20x = -100, -20

Detailed Explanation

Choice A is correct. Choice A is the correct answer. The x-intercepts occur where R(x)=0R(x) = 0. 1. Set the equation to zero: (100−x)(20+x)=0(100 - x)(20 + x) = 0. 2. Apply Zero Product Property: * 100−x=0⇒x=100100- x = 0 \Rightarrow x = 100 * 20+x=0⇒x=−2020+ x = 0 \Rightarrow x = -20 These points represent the prices or quantities where revenue is zero. Choice B is incorrect because of sign errors. Choice C is incorrect because 20+x=020 +x=0 gives −20-20. Choice D is incorrect because 100−x=0100 -x=0 gives 100100.

Key Steps:

•

The correct answer is x=100,−20x = 100, -20

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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