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3. Hallar el valor de " \( m \) " si \( P \) es un polinomio lineal. \[ P(x)=3 x+(3 m-15) x^{2}-11 \]

Ask by Craig Brooks. in Peru
Jan 22,2025

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El valor de \( m \) es **5**.

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Bonus Knowledge

Para que \( P(x) \) sea un polinomio lineal, el coeficiente de \( x^2 \) debe ser igual a cero. En este caso, el coeficiente de \( x^2 \) es \( 3m - 15 \). Entonces, igualamos a cero: \[ 3m - 15 = 0 \] Resolviendo para \( m \), sumamos 15 a ambos lados: \[ 3m = 15 \] Luego, dividimos entre 3: \[ m = 5 \] Por lo tanto, el valor de \( m \) que hace que \( P(x) \) sea un polinomio lineal es \( 5 \). Así que podemos decir que el polinomio se convierte en \( P(x) = 3x - 11 \), que efectivamente es lineal.

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