CAT 2025 Slot 1 QA Q7 Equations

Question 7 of the Quantitative Ability (QA) section, CAT 2025 Slot 1, with CAT's official answer and a worked solution.

The number of non-negative integer values of \(k\) for which the quadratic equation \(x^2-5 x+k=0\) has only integer roots, is

TITA: type in the answer. There are no options and no negative marking.

Answer: 3 Equations TITA

Solution

Integer roots \(p, q\) satisfy \(p + q = 5\) and \(pq = k \geq 0\).
With \(k \ge 0\), both roots are non-negative: \((0,5), (1,4), (2,3)\), giving \(k = 0, 4, 6\).
So there are 3 values.