Multiple choice

The condition for the equations $ax^{2} + bx + c = 0$ and $a'x^{2} + b'x + c' = 0$ to have reciprocal roots is $\dfrac{a}{c'}=\dfrac{b}{b'}=\dfrac{c}{a'}$

  1. True

  2. False
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A Correct answer
Explanation

For roots to be reciprocals, the product of roots must be 1. For ax^2+bx+c=0, product is c/a. For a'x^2+b'x+c'=0, product is c'/a'. If roots are reciprocals, c/a = a'/c', which rearranges to a/c' = a'/c. The given condition is a standard result for reciprocal roots.

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