Question

a(4,6) b(2,1) c(1,4)

Answer 1

I) -> (4^2)A + 4B + C = 6
II) -> (2^2)A + 2B + C = 1
III) -> (1^2)A + B + C = 4

III) - >A + B + C = 4
III) - > C = 4 - B - A

II) -> 4A + 2B + C = 1
II) -> 4A + 2B + 4 - B - A = 1
II) -> 3A + B + 4 = 1
II) -> 3A + B = 1 - 4
II) -> 3A + B = -3
II) -> B = -3 - 3A

C = 4 - B - A
C = 4 - (-3 - 3A) - A
C = 4 + 3 + 3A - A
C = 7 + 2A

I) -> 16A + 4B + C = 6
I) -> 16A + 4(-3 - 3A) + 7 + 2A = 6
I) -> 16A - 12 - 12A + 7 + 2A = 6
I) -> 6A - 5 = 6
I) -> 6A = 6 + 5
I) -> 6A = 11
I) -> A = 11/6
A = 1.83

B = -3 - 3A
B = -3 -3(1.83)
B = -3 - 5.49
B = -8.49

C = 7 + 2A
C = 7 + 2(1.83)
C = 7 + 3.66
C = 10.66

F(X) = 1.83X^2 - 8.49X + 10.66

S = {(1.83; -8.49; 10.66)}