6
advanced-math

If the roots of ax2+bx+c=0ax^2 + bx + c = 0 are reciprocals of each other, then:

A

a=ca = c

B

a=ba = b

C

b=cb = c

D

a=−ca = -c

Correct Answer: A

Choice A is the correct answer.

  1. Let the roots be rr and 1/r1/r.
  2. The product of roots is r×(1/r)=1r \times (1/r) = 1.
  3. From Vieta's formulas, Product = c/ac/a.
  4. So c/a=1c/a = 1, which implies c=ac = a.

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

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Set 12: Quadratic Equations and Functions 12