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  • How to solve this problem- If ABCD is a convex quadrilateral such that 4sec A + 5 = 0 then the quadratic equation whose roots are tan A and cosec A is

If ABCD is a convex quadrilateral such that 4sec A + 5 = 0 then the quadratic equation whose roots are tan A and cosec A is

  • Option 1)

    12x2 - 29x + 15 = 0

  • Option 2)

    12x2 - 11x -15 = 0

  • Option 3)

    12x2 + 11x - 15 = 0

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we learnt

 

Sign of Trigonometric Ratios -

 

All signs are positive or negative depending on the quadrants.

- wherein

 

 

 

secA = -5/4. So, p/2 < A < p. (Since the quadrilateral is convex).

Hence, tan A = -3/4 and cosec A = 5/3.

                        the required equation is x2 - \left( { - \frac{3}{4} + \frac{5}{3}} \right)$x + \left( { - \frac{3}{4}} \right)$ ´ \frac{5}{3}$= 0.

            or, 12x2 - 11x - 15 = 0


Option 1)

12x2 - 29x + 15 = 0

Option 2)

12x2 - 11x -15 = 0

Option 3)

12x2 + 11x - 15 = 0

Option 4)

none of these

Posted by

Himanshu

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