Question:medium

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?

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When given that roots are integers, always try to use the product and sum relations to create a factorable algebraic expression. Adding a constant to both sides to complete the factorization (Simon's Favorite Factoring Trick) is a very powerful technique in such integer-solution problems.

Updated On: May 22, 2026

$c - b$ is an integer multiple of $a$
Both the roots of the equation $ax^2 + bx + c = 0$ are odd integers
If $c = 15$, then $ab = 8$
If $b = 8$, then $x = 3$ is a root of the equation $ax^2 + bx + c = 0$

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The Correct Option is A

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