MHT CET 2024 Mathematics question

The equation in the variable x, has real roots. Then p can take any value in the interval

(A)
(B)
(C)
(D)Correct

Answer: (D)

Solution

Real roots need discriminant . Since , the second term has the sign of . For , so both terms are non-negative and always: real roots for every in . For a negative the second term is

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Question ID VK-092983