Multiple choice

If $\sec^2\frac {\pi}{7}$ & $\tan^2\frac {\pi}{7}$ are the roots of the equation $ax^2 + bx + c = 0$, then $\cfrac {5a^2-(b^2-c^2)}{(2a-c)^2}$ (wherever defined) is equal to

  1. $1$
  2. $2$
  3. $3$
  4. $4$
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A Correct answer
Explanation

Let x1 = sec^2(pi/7) and x2 = tan^2(pi/7). We know sec^2(theta) - tan^2(theta) = 1. The roots of ax^2 + bx + c = 0 satisfy x1 + x2 = -b/a and x1*x2 = c/a. Substituting these into the expression leads to the value 1.

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