Question

Determine os números complexos a e b para que o polinômio p(x) (2a +3b) x_4 (a-b+5) x3 seja identicamente nulo.​

Answer 1

$p(x) = (2a+3b)x^4 + (a-b+5)x^3\\\\2a + 3b = 0\\2a = -3b\\a = -\frac{3b}{2}\\\\a - b + 5 = 0\\-\frac{3b}{2}- b + 5 = 0\\-3b -2b + 10 = 0\\-5b = -10\\5b = 10\\b = \frac{10}{5}\\\boxed{b = 2}\\\\a = -\frac{3b}{2}\\a = -\frac{3 \cdot 2}{2}\\\boxed{a = -3}$