CAT 2020 Linear and Quadratic Equations Question (Medium)

Question

Let and be positive integers. If and have real roots, then the smallest possible value of is

Accepted Answer

Step 1 We are given two quadratic equations 1. 2. Both must have real roots, so their discriminants must be non-negative. For the first equation Delta_1 m 2 - 8n geq 0 For the second equation Delta_2 2n 2 - 4m geq 0 Delta_2 4n 2 - 4m geq 0 Rightarrow n 2 geq m Step 2 From the first From the second W

CAT 2020

Quantitative

Linear and Quadratic Equations

Medium

Let $m$ and $n$ be positive integers. If $x^2 + mx + 2n = 0$ and $x^2 + 2nx + m = 0$ have real roots, then the smallest possible value of $m + n$ is

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