Question
Determine the solution set of the following inequality: x3−x2≥25x−25
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Answer to a math question Determine the solution set of the following inequality: x3−x2≥25x−25
Darrell
4.5100 Answers
1. Reordenamos la inecuación:
x^3 - x^2 - 25x + 25 \geq 0
2. Factorizamos el polinomio.
3. El polinomio factorizado es:
(x^3 - x^2 - 25x + 25) = (x^2 - 25)(x - 1) = (x - 5)(x + 5)(x - 1)
4. Analizamos los intervalos críticos dados por las raíces:
(-\infty, -5), (-5, 1), (1, 5), (5, \infty)
5. Encontramos los signos del polinomio en cada intervalo crítico.
6. La inecuación original cumple en los siguientes intervalos:
(-\infty, -5] \cup [5, \infty)
Respuesta:(-\infty, -5] \cup [5, \infty)
2. Factorizamos el polinomio.
3. El polinomio factorizado es:
4. Analizamos los intervalos críticos dados por las raíces:
5. Encontramos los signos del polinomio en cada intervalo crítico.
6. La inecuación original cumple en los siguientes intervalos:
Respuesta:
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