5
advanced-math

Which equation has two distinct real roots?

A

x2+2x−1=0x^2 + 2x - 1 = 0

B

x2+2x+1=0x^2 + 2x + 1 = 0

C

x2+x+1=0x^2 + x + 1 = 0

D

x2+5=0x^2 + 5 = 0

Correct Answer: A

Choice A is the correct answer. We need Δ>0\Delta > 0.

  • A: 22−4(1)(−1)=4+4=82^2 - 4(1)(-1) = 4 + 4 = 8. (8>08 > 0, Two roots).
  • B: 22−4(1)(1)=4−4=02^2 - 4(1)(1) = 4 - 4 = 0. (One root).
  • C: 12−4(1)(1)=1−4=−31^2 - 4(1)(1) = 1 - 4 = -3. (No real roots).
  • D: 02−4(1)(5)=−200^2 - 4(1)(5) = -20. (No real roots).

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

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Set 11: Quadratic Equations and Functions 11