cat 2020 Question 23

Question

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

Accepted Answer

To have real roots the discriminant should be greater than or equal to 0.

So, $m^2 −8n$ ≥ 0 & $4n^2−4m$ ≥ 0

=> $m^2$ ≥ 8n & $n^2$ ≥ m

Since m, n are positive integers the value of m+n will be minimum when m=4 and n=2.

.'. m+n=6.

Question 23.