Question

Calcule os valores de a, b e c para os quais o polinômio P(x)=(a-12).x³+(b+a).x² + (b-c).x seja identicamente nulo.

Answer 1

$P(x) = (a-12)x^3+(b+a)x^2+(b-c)x \\ \\ a -12 = 0 \ \therefore \ \boxed{a = 12} \\ b + a = 0 \implies b + 12 = 0 \ \therefore \ \boxed{b = -12} \\ b-c = 0 \implies -12 - c = 0 \ \therefore \ \boxed{c = -12}$