Quadratic Equations
Integer Roots
JEE Advanced
Grade 11
Question:
If $x^2 + px - 444p = 0$ has integer roots where $p$ is a prime number, then $p$ equals:
(1) $2$
(2) $3$
(3) $7$
(4) $37$
Step-by-Step Solution
Key Concept: For integer roots the discriminant $D = p^2 + 1776p = p(p+ 1776)$ must be a perfect square. This forces $p \mid 1776$. Factorise 1776 to find prime divisors and test each.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (4)