CAT 2025

Slot 1

QA

Question & Solution

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 $$k=4$$, $$D=25-4\times4=25-16=9$$, is a perfect square

For $$k=6$$, $$D=25-4\times\ 6=1$$, is a perfect square

So, there are three non negative integer values of $$k$$.

So, correct answer is $$3$$.