Question

Detetermine a,b e c par que o polinomio P (x)=2ax^2+ax-bx+a+6x^2-2x+c+2 seja identicamente nulo.

Answer 1

P (x)=2ax^2+ax-bx+a+6x^2-2x+c+2
2ax^2+ax-bx+a+6x^2-2x+c+2 = 0 2ax^2+6x^2+ax-bx-2x+a+c+2 = 0(2a+6)x^2+ (a-b-2)x+a+c+2 = 0
2a + 6 = 0 ==> 2a = - 6 ==> a = - 3
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a - b - 2 = 0 ==> b = a - 2 ==> b = - 3 - 2 ==> b = - 5
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a + c + 2 = 0==> c = - a - 2 ==> c = -(-3) - 2==>c = 3 - 2 ==> c = 1