Multiple choice

For what value of $k$ will the equation $\dfrac { x ^ { 2 } - b x } { a x - c } = \dfrac { k - 1 } { k + 1 }$ have roots reciprocal to each other?

  1. $\dfrac { c - 1 } { 1 + c }$
  2. $\dfrac { c + 1 } { c - 1 }$
  3. $a - c$
  4. $\dfrac { b + c } { c - 1 }$
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A Correct answer
AI explanation

If the roots of the quadratic are reciprocal to each other, their product must equal 1. Clearing the fraction gives the quadratic equation (k+1)x^2 - (bk+c+c k-b)x - c(k-1) = 0. Using the product of roots formula, c/(1-k) = 1, which simplifies directly to k = (c-1)/(c+1).

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