Question

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

Answer 1

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.

Answer 2

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