Respostas

2014-07-30T10:10:19-03:00
p(X)  = ax³ + bx² + cx + d

--------------
p(0)=12
a . 0³ + b . 0² + c . 0 + d = 12
d = 12

-------------

p(-1)=0
a.(-1)³ + b . (-1)² + c . (-1) + d = 0
-a + b - c + d = 0
-a + b - c + 12 = 0
-a + b - c = -12
------------

p(3)=0
a . 3³ + b . 3² + c . 3 + d = 0
27a + 9b + 3c + 12 = 0
27a + 9b + 3c = -12
9a + 3b + c = -4
------------

p(-2) = 0
a . (-2)³ + b . (-2)² + c . (-2) + d = 0
-8a + 4b - 2c + 12 = 0
-8a + 4b - 2c = -12
-4a + 2b - c = -6
------------

-a + b - c = -12
9a + 3b + c = -4
-4a + 2b - c = -6
-------------
soma a primeira à segunda:
8a + 4b = -16
2a + b = -4
-------------
soma a segunda à terceira:
5a + 5b = -10
a + b = -2
-------------
2a + b = -4
a + b = -2

multiplica a segunda por -1:

2a + b = -4
-a - b = 2

soma:
a = -2
-------------------------
a + b = -2

-2 + b = -2
b = 0
-------------------------
-a + b - c = -12
- (-2) + 0 - c = -12
2 - c = -12
-c = -14
c = 14
------------------------
ax³ + bx² + cx + d = p(x)
-2x³ + 14x + 12 = p(x)
-----------------------
p(1) = -2.1³ + 14.1 + 12
p(1) = -2 + 14 + 12
p(1) = 12 + 12
p(1) = 24










1 5 1