Question

Calcule a, b, c para que se tenha um polinômio (x) = (a + b) x^2 + (a - b - 4) x + (b +2c - 8) seja identicamente nulo.

Answer 1

a+ b = 0
a - b - 4 = 0
b + 2c -8 = 0

a + b = 0
a - b = 4
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2a = 4
a = 4/2
a = 2

a + b = 0
2 + b = 0
=> b = -2

b - 2c = 8
-2 - 2c = 8
-2c = 8+2
-2c = 10
c = 10/-2 => c = -5

Answer 2

polinômio (x) = (a + b) x^2 + (a - b - 4) x + (b +2c - 8) seja identicamente nulo.

a + b = 0
a - b -4 =0
b +2c - 8 = 0

a + b = 0
a - b = 4 
 2a = 4 ==> a = 2
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b = - a ==> b = - 2
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b +2c - 8 = 0 ==> 2c = 8 - b ==. 2c = 8 -(-2)==>

2c = 8+2 ==> 2c = 10 ==> c = 5
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P(x) = (a + b) x^2 + (a - b - 4) x + (b +2c - 8) 

a =  2    ;  b =  - 2    ;  c = 5

P(x) = (2 - 2) x^2 + ( 2 -(-2) - 4) x + ( -2 +2(5) - 8) 

P(x) = (2 - 2)x^2 + ( 2+2 - 4) x + ( -2 + 10 - 8) = 0