CAT 2024 Question Paper | Quant Slot 1

CAT Questions

CAT 2024 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 20 :If the equations $x^2+m x+9=0, x^2+n x+17=0$ and $x^2+(m+n) x+35=0$ have a common negative root, then the value of $(2 m+3 n)$ is

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Video Explanation

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Explanatory Answer

Let the root be $x=p$ $$p^2+m p+9=p^2+m p+n p+35=p^2+n p+17=0$$ Equating the terms, we get $$\begin{array}{l} n p+35=9 ; n p=-26 \\ m p+35=17 ; m p=-18 \\ p^2-18+9=0 \\ p^2=9 \\ p=-3 \\ m=-18 /-3=6 \\ n=-26 /-3=26 / 3 \\ 2 m+3 n=2(6)+3(26 / 3)=12+26=38 \end{array}$$

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The question is "If the equations $x^2+m x+9=0, x^2+n x+17=0$ and $x^2+(m+n) x+35=0$ have a common negative root, then the value of $(2 m+3 n)$ is"

Hence, the answer is '38'

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