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Question

If the equation cot to the power of 4 space x minus 2 cos space e c squared x plus a squared =0 has at least one solution, then the sum of all possible integral values of 'a' is equal to

  1. 4
  2. 3
  3. 2
  4. 0

Hint:

In the question, the equation cot to the power of 4 space x minus 2 cos space e c squared x plus a squared =0 has at least one solution, and we have to find the sum of all possible integral values of 'a'. firstly, we will find the real solution of the given equation, using which we can find the range of a and later analyzing that we can find the sum of all possible integral values of a.

The correct answer is: 0


    G i v e n comma space cot to the power of 4 space x minus 2 cos e c squared x plus a squared equals 0
rightwards double arrow c o t to the power of 4 x minus 2 open parentheses 1 plus c o t squared x close parentheses plus a squared equals 0
rightwards double arrow c o t to the power of 4 x minus 2 c o t squared x plus a squared minus 2 equals 0
rightwards double arrow c o t squared x equals fraction numerator 2 plus-or-minus square root of 4 minus 4 open parentheses a squared minus 2 close parentheses end root over denominator 2 end fraction
f o r space r e a l space r o o t comma space
4 minus 4 open parentheses a squared minus 2 close parentheses greater than 0
1 minus open parentheses a squared minus 2 close parentheses greater than 0
1 minus a squared plus 2 greater than o
3 minus a squared greater than 0
3 greater than a squared
plus-or-minus square root of 3 greater than a
t h e r e f o r e comma a element of open parentheses negative square root of 3 comma square root of 3 close parentheses
S o comma space s u m space o f space v a l u e s space o f space a equals 0.

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