Multiple choice

If ABCD is a cyclic quadrilateral such that $\displaystyle 12\tan A-5$ and $5\cos B+3=0$ then the quadratic equation whose roots are $\displaystyle \cos C,\tan D$ is

  1. $\displaystyle 39x^{2}-16x-48=0$
  2. $\displaystyle 39x^{2}+88x-48=0$
  3. $\displaystyle 39x^{2}-88x+48=0$

  4. none of these
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A Correct answer
Explanation

Interpreting the first condition as 12 tan A - 5 = 0 gives tan A = 5/12, so cos A = 12/13. The second condition gives cos B = -3/5 and tan D = 4/3 because A + C = 180 degrees and B + D = 180 degrees. The roots are -12/13 and 4/3, producing 39x^2 - 16x - 48 = 0.

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