CAT 2025 Question Paper | Quant Slot 1

CAT Questions

CAT 2025 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 7 : 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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Video Explanation

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Explanatory Answer

Let the integer roots of the equation be \(P\) and \(Q\):

\(P+Q=5\)
\(P\times Q=k\)

Since \(P\) and \(Q\) are integers whose sum is 5, the possible non-negative integer values for \(k\) are obtained by multiplying the complementary pairs \(5,0\), \(4,1\), and \(3,2\):

\(5\times0=0\)
\(4\times1=4\)
\(3\times2=6\)

Thus, the distinct non-negative integer values for \(k\) are \(0,4,6\), giving a total of 3 values.

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The question is " 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 "

Hence, the answer is '3'

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