CAT 2024 Linear and Quadratic Equations Question (Hard)

Question

If the equations , and have a common negative root, then the value of is

Accepted Answer

Step 1 Let the common negative root be . Then it satisfies all three 1. 2. 3. From 1 and 3 m n p 35 mp 9 implies np 35 9 implies np -26 quad i From 2 and 3 m n p 35 np 17 implies mp 35 17 implies mp -18 quad ii --- Step 2 Use ii in 1 p 2 - 18 9 0 implies p 2 9 implies p -3 quad --- Step 3 Use in ii

CAT 2024

Quantitative

Linear and Quadratic Equations

Hard

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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