5
advanced-math

For what kk does y=x2+ky = x^2 + k intersect y=2xy = 2x exactly once?

A

1

B

-1

C

0

D

4

Correct Answer: A

Choice A is the correct answer.

  1. Set equal: x2+k=2xx^2 + k = 2x.
  2. Standard form: x2−2x+k=0x^2 - 2x + k = 0.
  3. For one intersection, Δ=0\Delta = 0.
  4. (−2)2−4(1)(k)=0(-2)^2 - 4(1)(k) = 0.
  5. 4−4k=0⇒k=14 - 4k = 0 \Rightarrow k = 1.

Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

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Set 15: Quadratic Equations and Functions 15