Answer:
a = 3, b = -1 and c = -2.
Step-by-step explanation:
By the Remainder Theorem If the remainder is 2 then f(-1) = 2 ( as its divided by x+1), and if remainder = 8 then f(2) = 8.
When divide by x - 1 the remainder = 0 so f(1) = 0.
So we have the system:
a(-1)^2 + b*-1 + c = 2
a(2)^2 + b * 2 + c = 8
a(1)^2 + b * 1 + c = 0
a - b + c = 2 (A)
4a + 2b + c = 8 (B)
a + b + c = 0 (C)
Adding A and C gives:
2a + 2c = 2 (D)
a + c = 1 (E)
Multiplying A by 2 and adding to B gives:
6a + 3c = 12
2a + c = 4 (F)
Subtract F - E gives:
2a - a = 4 - 1
a = 3
so c = 1 - 3 = -2.
Substituting for a and c in equation C:
3 - b - 2 = 0
b = -1.
