Respuesta :
m = 5 and n = 3
let f(x) = 2x³ - mx² + nx - 2 , then
f( - 1 ) = - 2 - m - n - 2 = - 12
f(2 ) = 16 - 4m + 2n - 2 = 0
Tidying up the 2 equations
- m - n = - 8 → (1)
- 4m + 2n = - 14 → ( 2)
multiply equation ( 1) by 2
- 2m - 2n = - 16 → ( 3 )
add ( 2 ) and ( 3 ) term by term
-6m = - 30 ⇒ m = 5 ( substitute m = 5 into (2 )
- 20 + 2n = - 14
2n = 6 ⇒ n = 3
Hey there!!
Using the remainder theorem :
x + 1 = 0
x = -1
The remainder is -12.
Plugging in the values :
... 2x³ - mx² + nx - 2 = -12
... 2x³ - mx² + nx = - 10
... 2 ( - 1 )³ -m ( -1 )² + n ( -1 )
... -2 - m - n = - 10
... - m - n = -8
Let's take the other one :
x - 2 = 0
x = 2
Plugging in the values :
2x³ - mx² + nx - 2 = 0
2x³ - mx² + nx = 2
2 ( 2 )³ - m ( 2 )² + n ( 2 ) = 2
16 - 4m + 2n = 2
- 4m + 2n = -14
Let's get both the equations together :
- m - n = -8 ---- ( 1 )
- 4m + 2n = -14 ---- ( 2 )
......................................................................................................................................................................
Multiply the first equation with 2
- 2m - 2n = -16 --- ( 1 )
- 4m + 2n = -16 --- ( 2 )
Add both the equations.
...................................................................................................................................................................... - 6m = - 32
m = -32 / - 6
m = 32 / 6
m = 16 / 3
Substitute this value to get the value of ' n '
- m - n = - 8
- 16 / 3 - n = - 8
- n = - 8 + 16 / 3
- n = - 8 / 3
n = 8 / 3
m = 16 / 3 and n = 8 / 3
Hope my answer helps!!
