CAT 2025 Linear and Quadratic Equations Question (Hard)

Question

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

Accepted Answer

The given quadratic equation is x 2-5x k 0 Now, discriminant D 5 2-4k 25-4k Now, it is given the equation must have integer roots. So, 25-4k has to be a perfect square. We need to find non-negative integer values of k Now, for k 0, D 25-4 times 0 25, is a perfect square For k 4, D 25-4 times4 25-16

CAT 2025

Quantitative

Linear and Quadratic Equations

Hard

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

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