Question

determine m e n de modo que o polinômio p (x) = (m² - 16)x^4 - (3m + n)x², seja identicamente nulo.

Answer 1

Vejamos:


P(x) = (m^2 - 16)x^4 - (3m + n)x^2


Logo:


*m^2 - 16 = 0                         *3m + n = 0               *3m + n = 0

m^2 = 16                                 3 . 4 + n = 0              3 . (-4) + n = 0

m = +-V16                               12 + n = 0                 -12 + n = 0

m = +-4                                    n = -12                      n = 12


m = {4, -4}                                                     n = {12, -12}