Question

What is the solution set for the equation?


x^2+2x−24=0

Answer 1

x = - 6 or x = 4

Explanation:

x^2 + bx + c = 0

x^2 + 2x − 24 = 0

Using factorization,

x^2 + bx + c = (x +
`n_(1)`)(x +
`n_(2)`)

`n_(1)` ×
`n_(2)` must = c

`n_(1)` +
`n_(2)` must = b

c =
`n_(1)` ×
`n_(2)`

= 6 × - 4

= 24

b =
`n_(1)` +
`n_(2)`

= 6 + - 4

= 6 - 4

= 2

(x +
`n_(1)`)(x +
`n_(2)`) = 0

(x + 6)(x - 4) = 0

x + 6 =
`(0)/(x - 4)`

x + 6 = 0

x = - 6

OR

x - 4 =
`(0)/(x +6)`

x - 4 = 0

x = 4