A student while solving a quadratic equation in \(x\), he copied its constant term incorrectly and got its roots as 5 and 9. Another student copied the constant term and coefficient of \(x^2\) of the same equation correctly as 12 and 4 respectively. If \(s, p\) and \(\Delta\) denote respectively the sum of the roots, the product of the roots and the discriminate of the correct equation, then \(\frac{\Delta}{3 p+s}=\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.