Question

find n. (n!)²- 4n! - 12 = 0​

Answer 1

Answer:

n=6 , n=-2

Step-by-step explanation:

$n^{2}-4n-12=0$

Factorise to give:

$(n-6)(n+2)$

Set first one to equal 0:

$n-6=0$

$n=6$

Set second one to equal 0:

$n+2=0$

$n=-2$

Reason for 2 solutions:

All quadratics can have a maximum of 2 solutions like this one or a minimum of 0.

The solution(s) is the point where the graph crosses the x-axis

The image below shows the graph of the equation:

$n^{2}-4n-12$

When y=0:

It intercepts the x-axis at 6 and -2 giving why n has 2 solutions