Reciprocal roots condition (standard form): For the quadratic ax^2 + bx + c = 0 with nonzero roots, the roots are reciprocals of each other if and only if:

Introduction / Context:
If r and s are the roots of ax^2 + bx + c = 0, then r*s = c/a by Vieta. The roots are reciprocals of each other precisely when r*s = 1 and both are nonzero, which directly translates to c/a = 1 ⇒ c = a. This is a textbook criterion for reciprocal roots.

Given Data / Assumptions:

• Quadratic: ax^2 + bx + c = 0.
• Roots are real or complex but nonzero.

Concept / Approach:
Use the product of roots formula. The reciprocity condition requires the product to equal 1, hence c/a = 1.

Step-by-Step Solution:

Verification / Alternative check:
Consider transformed polynomial with roots 1/r and 1/s. Its monic form relates coefficients by swapping a and c, reinforcing the symmetry when c = a.

Why Other Options Are Wrong:

• a = b or b = c: Do not constrain the product to be 1.
• None of these: Incorrect; c = a is the correct and sufficient condition.

Common Pitfalls:
Overlooking the nonzero requirement (a root 0 breaks reciprocity) or confusing with the equal-roots discriminant condition.

Final Answer: