If _1, _2, _3, _4 are roots of the equation ( + )=k 2 , no two of which differ by a multiple of 2 , then _1+ _2+ _3+ _4 is equal to

JEE Main Mathematics question

Not in JEE Main syllabus

If are roots of the equation , no two of which differ by a multiple of , then is equal to

(A)
(B)Correct
(C)
(D)None of these

Answer: (B)

Solution

Write the equation with ; both and become rational functions of , and clearing denominators gives a quartic in . The four roots satisfy relations from which

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Question ID VK-008562