Question

Determine 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.

✔️✔️NO SPAMMING✔️✔️​

Answer 1

Solution:-

Refer to the Attachment!!

Answer 2

Answer:

Step-by-step explanation:

here A = 2a^2

       B = 2anc

       C = [n^2-2]c^2

to get real roots  the discriminant should be non negative

   B^2 -4AC  ≥ 0

4a^2n^2c^2  - 4 [2a^2] [n^2-2]c^2 ≥ 0

divide by  4a^2c^2

n^2  -  [2] [n^2-2] ≥ 0

n^2  -  2n^2   +4  ≥ 0

- n^2  +4  ≥ 0

4  ≥  n^2

-2 ≤ n ≤ 2

limits of n is [ -2   ,  2]