Question

The limits between which $n$ must lie in order that the equation $2ax(ax+nc)+(n^2-2)c^2=0$ may have real roots is

• A. [$3$, $10$]
• B. [$-1$, $3$]
• C. [$2$,$5$]
• D. [$-2$,$2$]

Answer 1

Answer: (D)

[$-2$,$2$]

Given that $2ax(ax+nc)+(n^2-2)c^2=0$ have real roots

$2a^2{x}^2+2ancx+(n^2-2)c^2=0$

$\therefore △\ge 0$

$\therefore 4a^2{c}^2{n}^2-4\left(2a^2\right)(n^2-2)c^2\ge 0$

$4a^2{c}^2(n^2-2n^2+4)\ge 0$

$-n^2+4\ge 0$

$\therefore n^2-4\le 0$

$\therefore nϵ[-2,2]$

$\therefore n$ lie between $-2$ and $2$