Answer:
Option (d) is correct.
The solution of given quadratic equation \(n^2+2n-24=0\) is 4 and -6.
Step-by-step explanation:
Given equation \(n^2+2n-24=0\)
We have to solve using factorization.
Consider the given quadratic equation \(n^2+2n-24=0\)
We can solve the quadratic equation using middle term splitting method,
Split the middle term in such a away that the product of term gives the product of coefficient of two other terms.
Thus, 2n can be written as 6n-4n,
We have \(n^2+2n-24=0\)
\(\Rightarrow n^2+6n-4n-24=0\)
Taking n common from first two term and -4 common from last two terms, we have,
\(\Rightarrow n(n+6)-4(n+6)=0\)
taking (n + 6) common, we have,
\(\Rightarrow (n-4)(n+6)=0\)
Using , zero product property ,
\(a\cdot b=0 \Rightarrow a=0 \ or\ b=0\) we have,
\(\Rightarrow (n+6)=0\) or \(\Rightarrow (n-4)=0\)
On simplify, we have,
\(\Rightarrow n=-6\) or \(\Rightarrow n=4\)
Thus, the solution of given quadratic equation \(n^2+2n-24=0\) is 4 and -6.
Option (d) is correct.
