Let a,b,c be positive integers in arithmetic progression such that the equation ax^2+bx+c=0 has only integer solutions. Then which of the following statements is (are) TRUE ?

JEE Advanced 2026 Mathematics question

Let be positive integers in arithmetic progression such that the equation

+bx+c=0

has only integer solutions.

Then which of the following statements is (are) TRUE ?

Answer: (A),(B),(C)

Since , both roots are negative; write them as and with positive integers. Then

p+q=, pq=.

The AP condition is , i.e. , so

2(p+q)=1+pq\ \ pq-2p-2q+4=3\ \ (p-2)(q-2)=3 .

For positive integers the only possibility is

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Question ID VK-104758