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

• A. 7
• B. 8
• C. 5
• D. 6

Answer 1

Answer: (D)

6

Answer 2

The correct answer is (D): $6$

Since the roots are real $m^2-8n≥0$ and $(2n)^2-4m≥0 ⇒ n^2-m≥0$

$⇒ n^4≥m^2≥8n$

$⇒ n≥2$ and $m≥4$

Hence the least value of $m+n=2+4=6$