Question

raízes do polinômio p(x)=x3-3x2-13x+15.

Answer 1

Resposta:

$\boxed{\mathbb{S}=\left\{-3,1,5\right\}}$

Explicação passo-a-passo:

$\boxed{f(x)=x^3-3x^2-13x+15}$

$f(1)=1-3-13+15=16-16=0\ \to\ \boxed{x=1}\ \mathrm{\acute{e}\ raiz\ de}\ f(x).$

$\text{Dispositivo\ de\ Briot-Ruffini:}\\\\ \left\begin{array}{c}1&&&\end{array}\right|\left \begin{array}{cccc}1&-3&-13&15\\&1&-2&-15\\1&-2&-15&0\end{array}\right|$

$\boxed{f(x)=(x-1)(x^2-2x-15)}$

$x^2-2x-15=0\ \therefore\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\ \therefore$

$x=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(-15)}}{2(1)}=\dfrac{2\pm8}{2}=1\pm4\ \therefore$

$\boxed{x=5}\ \text{e}\ \boxed{x=-3}\ \mathrm{s\tilde{a}o\ ra\acute{i}zes\ de}\ f(x).$