Question

The number of integers ${}^{\prime }{n}^{\prime }$ such that the equation $n{x}^2+(n+1)x+(n+2)=0$ has rational roots only, is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

$n{x}^2+(n+1)x+(n+2)=0$ has rational roots

When discriminated $\left(D\right)$ is a perfect square no.

$D={(n+1)}^2-4n(n+2)$

$=n^2+2n+1-4n^2-8n$

$=1-6n+4n^2$

$\therefore n=0$ is the only solution.