Question

(UFSC) Para que o polinômio P(x) = (a+b)x² + (a - b + c)x + (b + 2c - 6) seja identicamente nulo, o valor de c deve ser:
a) 4
b) 4,8
c) 1,2
d) 2,4

Answer 1

P(x) = (a + b)x² + (a - b + c)x + (b + 2c - 6) = 0x² + 0x + 0
a + b = 0 => a = -b
a - b + c = 0 => (-b) - b + c = 0 => -2b + c = 0 => -2b = -c => 2b = c => b = c/2
b + 2c - 6 = 0 => c/2 + 2c - 6 = 0 => x/2 + 4c/2 = 6 => 5c/2 = 6 => 5c = 6 x 2 = 12 => c = 12/5 = 2,4 (D)