Barrett Byrd
05/24/2023 · Elementary School
40. Sea el polinomio \( h(x)=\frac{1}{4} x^{8}-\frac{1}{4} x^{7}-\frac{3}{4} x^{6}+\frac{1}{4} x^{5}+\frac{1}{2} x^{3}+a x^{2} \) a) Obtener el valor de a \( \epsilon \mathrm{R} \) considerando que \( \sqrt{2} \) es una raiz de \( \mathrm{h}(\mathrm{x}) \). b) Aplicar la regla de los signos de Descartes para determinar las diferentes posibilidades en que se pueden presentar sus raices. c) Determinar todas las raices.
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a) \( a = -\frac{1}{2} + \frac{1}{4}\sqrt{2} \)
b) Posibilidades de raíces: 3, 1 o 0 positivas; 2, 0 o 1 negativas.
c) Para encontrar todas las raíces, se recomienda el uso de software o métodos numéricos.
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