Answer:
n = -5 or -6
Step-by-step explanation:
[tex]n^2+ 11n + 30 = 0[/tex]
Lets factorise the quadratic equation :-
→ Lets split the middle term of the equation.
[tex]=> n^2 + 5n + 6n + 30 = 0[/tex]
→ Lets take 'n' common from the first 2 terms & '6' common from last 2 terms.
[tex]=> n(n + 5) + 6(n + 5) = 0[/tex]
→ Lets take (n + 5) whole in common from the equation.
[tex]=> (n + 5)(n + 6) = 0[/tex]
Here , we get 2 values of n :-
1) [tex]n + 5 = 0[/tex]
[tex]=> n = -5[/tex]
2) [tex]n + 6 = 0[/tex]
[tex]=> n = -6[/tex]
∴ Hence , n = -5 or -6
