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3 votes
7. Solve by factoring. n² + 2n – 24 = 0 (1 point). A. –12, 2. B.–2, 12. C.–6, 4. D.–4, 6

User Elza
by
7.0k points

2 Answers

3 votes

Answer:

Option (d) is correct.

The solution of given quadratic equation
n^2+2n-24=0 is 4 and -6.

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.

User Tony Borres
by
5.9k points
3 votes
n² + 2n – 24=0
n² + 6n-4n – 24=0
n(n + 6) – 4(n+6)=0
(n+6)(n-4)=0
Hence,
n=4
or
n=-6
User Jberrio
by
6.0k points
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