Harrington Sullivan
05/22/2023 · Primary School
1. Si la suma de coefici \( K(x)=(a+2) x^{a-3}+(a+1) x^{a-2}+(a+3) x^{a-1} \) es 21 , calcular su grado absoluto.
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Para calcular el grado absoluto del polinomio \( K(x) \), primero necesitamos determinar el valor de \( a \) que hace que la suma de los coeficientes sea 21. El polinomio se da por:
\[ K(x) = (a+2)x^{a-3} + (a+1)x^{a-2} + (a+3)x^{a-1} \]
La suma de los coeficientes es:
\[ (a+2) + (a+1) + (a+3) = 21 \]
Para encontrar \( a \), resolvemos la ecuación:
\[ 3a + 6 = 21 \]
\[ 3a = 21 - 6 \]
\[ 3a = 15 \]
\[ a = 5 \]
Ahora que sabemos que \( a = 5 \), podemos escribir el polinomio \( K(x) \) con el valor de \( a \):
\[ K(x) = (5+2)x^{5-3} + (5+1)x^{5-2} + (5+3)x^{5-1} \]
\[ K(x) = 7x^2 + 6x^3 + 8x^4 \]
El grado absoluto de un polinomio es el mayor exponente de las variables en el polinomio. En este caso, el mayor exponente es 4, por lo que el grado absoluto del polinomio \( K(x) \) es 4.
Quick Answer
El grado absoluto del polinomio \( K(x) \) es 4.
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