Question

qual deve ser o o velor d o para que o polinômio p(x)=(k2-81)x5 (kx2+3x-4x tenho grau 3?​

Answer 1

Resolução:

$p(x)=(k2-81)x5 (kx2+3x-4x$

$\left\{\begin{matrix}k=-\frac{x\left(-k_{2}x_{5}+81x_{5}-p\right)}{x_{2}x_{5}\left(k_{2}-81\right)}\text{, }&k_{2}\neq 81\text{ and }x_{2}\neq 0\text{ and }x_{5}\neq 0\\k\in \mathrm{R}\text{, }&\left(p=0\text{ and }x_{5}=0\right)\text{ or }\left(x=0\text{ and }x_{5}=0\right)\text{ or }\left(x=0\text{ and }k_{2}=81\text{ and }x_{5}\neq 0\right)\text{ or }\left(p=0\text{ and }k_{2}=81\text{ and }x_{5}\neq 0\right)\text{ or }\left(p=x_{5}\left(81-k_{2}\right)\text{ and }x_{2}=0\text{ and }k_{2}\neq 81\text{ and }x_{5}\neq 0\right)\text{ or }\left(x=0\text{ and }x_{2}=0\text{ and }k_{2}\neq 81\text{ and }x_{5}\neq 0\right)\end{matrix}\right.$

Observação:

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