2. Obtener las soluciones de las siguientes ecuaciones cuadráticas utilizando la fórmula general : a. X ^ 2 + 2x - 8 = 0 b. 4x ^ 2 + 12x - 8 = 0 c. 〖5x〗 ^ 2 + 6x + 1 = 0 d. 〖2x〗 ^ 2 + 5x - 12 = 0 e. X ^ 2 - 8x + 16 = 0.
ax² + bx + c = 0
En resumen
A. <img src="https://tex.z-dn.net/?
A. <img src="https://tex.z-dn.net/?f=x%5E%7B2%7D%2B2x-8%3D0%5C%5C%20%5C%5Ca%3D1%3B%20b%3D2%20%3Bc%3D-8%5C%5C%5C%5Cx%3D%5Cfrac%7B-b%C2%B1%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D%5C%5C%20%5C%5CReemplazamos%3A%5C%5C%5C%5C%20x%3D%5Cfrac%7B-2%C2%B1%5Csqrt%7B2%5E%7B2%7D-4%2A1%2A-8%7D%7D%7B2%2A1%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B-2%C2%B1%5Csqrt%7B4%2B32%7D%7D%7B2%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B-2%C2%B1%5Csqrt%7B36%7D%7D%7B2%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B-2%C2%B16%7D%7B2%7D%5C%5C%5C%5Cx1%3D%5Cfrac%7B-2%2B6%7D%7B2%7D%5C%5C%20%5C%5Cx1%3D%5Cfrac%7B4%7D%7B2%7D%5C%5C%20%5C%5Cx1%3D2%5C%5C%5C%5Cx2%3D%5Cfrac%7B-2-6%7D%7B2%7D%5C%5C%20%5C%5Cx2%3D%5Cfrac%7B-8%7D%7B2%7D%5C%5C%20%5C%5Cx2%3D-4" />B.
<img src="https://tex.z-dn.net/?f=4x%5E%7B2%7D%2B12x-8%3D0%5C%5C%20%5C%5Ca%3D4%3B%20b%3D12%20%3Bc%3D-8%5C%5C%5C%5Cx%3D%5Cfrac%7B-b%C2%B1%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D%5C%5C%20%5C%5CReemplazamos%3A%5C%5C%5C%5C%20x%3D%5Cfrac%7B-12%C2%B1%5Csqrt%7B12%5E%7B2%7D-4%2A4%2A-8%7D%7D%7B2%2A4%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B-12%C2%B1%5Csqrt%7B144%2B128%7D%7D%7B8%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B-12%C2%B1%5Csqrt%7B272%7D%7D%7B8%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B-12%C2%B116%2C5%7D%7B8%7D%5C%5C%5C%5Cx1%3D%5Cfrac%7B-12%2B16%2C5%7D%7B8%7D%5C%5C%20%5C%5Cx1%3D%5Cfrac%7B4%2C5%7D%7B8%7D%5C%5C%20%5C%5Cx2%3D%5Cfrac%7B-12-16%2C5%7D%7B8%7D%5C%5C%20%5C%5Cx2%3D%5Cfrac%7B-28%2C5%7D%7B8%7D%5C%5C" />C.
<img src="https://tex.z-dn.net/?f=5x%5E%7B2%7D%2B6x%2B1%3D0%5C%5C%20%5C%5Ca%3D5%3B%20b%3D6%20%3Bc%3D1%5C%5C%5C%5Cx%3D%5Cfrac%7B-b%C2%B1%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D%5C%5C%20%5C%5CReemplazamos%3A%5C%5C%5C%5C%20x%3D%5Cfrac%7B-6%C2%B1%5Csqrt%7B6%5E%7B2%7D-4%2A5%2A1%7D%7D%7B2%2A5%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B-6%C2%B1%5Csqrt%7B36-20%7D%7D%7B10%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B-6%C2%B1%5Csqrt%7B16%7D%7D%7B10%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B-6%C2%B14%7D%7B10%7D%5C%5C%5C%5Cx1%3D%5Cfrac%7B-6%2B4%7D%7B10%7D%5C%5C%20%5C%5Cx1%3D%5Cfrac%7B-2%7D%7B10%7D%5C%5C%20%5C%5Cx1%3D-0%2C2%5C%5C%5C%5Cx2%3D%5Cfrac%7B-6-4%7D%7B10%7D%5C%5C%20%5C%5Cx2%3D%5Cfrac%7B-10%7D%7B10%7D%5C%5C%20%5C%5Cx2%3D-1" />D.
<img src="https://tex.z-dn.net/?f=2x%5E%7B2%7D%2B5x-12%3D0%5C%5C%20%5C%5Ca%3D2%3B%20b%3D5%20%3Bc%3D-12%5C%5C%5C%5Cx%3D%5Cfrac%7B-b%C2%B1%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D%5C%5C%20%5C%5CReemplazamos%3A%5C%5C%5C%5C%20x%3D%5Cfrac%7B-5%C2%B1%5Csqrt%7B5%5E%7B2%7D-4%2A2%2A-12%7D%7D%7B2%2A2%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B-5%C2%B1%5Csqrt%7B25%2B96%7D%7D%7B4%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B-5%C2%B1%5Csqrt%7B121%7D%7D%7B4%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B-5%C2%B111%7D%7B4%7D%5C%5C%5C%5Cx1%3D%5Cfrac%7B-5%2B11%7D%7B4%7D%5C%5C%20%5C%5Cx1%3D%5Cfrac%7B6%7D%7B4%7D%5C%5C%20%5C%5Cx1%3D1%2C5%5C%5C%5C%5Cx2%3D%5Cfrac%7B-5-11%7D%7B4%7D%5C%5C%20%5C%5Cx2%3D%5Cfrac%7B-16%7D%7B4%7D%5C%5C%20%5C%5Cx2%3D-4" />E.
<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D-8x%2B16%3D0%5C%5C%20%5C%5Ca%3D1%3B%20b%3D-8%20%3Bc%3D16%5C%5C%5C%5Cx%3D%5Cfrac%7B-b%C2%B1%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D%5C%5C%20%5C%5CReemplazamos%3A%5C%5C%5C%5C%20x%3D%5Cfrac%7B-%28-8%29%C2%B1%5Csqrt%7B%28-8%29%5E%7B2%7D-4%2A1%2A16%7D%7D%7B2%2A1%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B8%C2%B1%5Csqrt%7B64-64%7D%7D%7B2%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B8%C2%B1%5Csqrt%7B0%7D%7D%7B2%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B8%C2%B10%7D%7B2%7D%5C%5C%5C%5Cx1%3D%5Cfrac%7B8%2B0%7D%7B2%7D%5C%5C%20%5C%5Cx1%3D%5Cfrac%7B8%7D%7B2%7D%5C%5C%20%5C%5Cx1%3D4%5C%5C%5C%5Cx2%3D%5Cfrac%7B-8-0%7D%7B2%7D%5C%5C%20%5C%5Cx2%3D%5Cfrac%7B-8%7D%7B2%7D%5C%5C%20%5C%5Cx2%3D-4" />.
Espero haberte ayudado.
Esta es la fórmula general, no olvides que las letras a, b y c son los coeficientes de la ecuación que va así : .
Respuesta : Fórmula general. Consideremos la ecuación general de segundo grado (ecuación cuadrática) que tiene la forma : a x 2 + b x + c = 0 Explicación paso a paso :
Respuesta : Explicación paso a paso : Le das los valores, multiplicas la b ^ 2 - cuatro multiplicas por a y c y lo mismo con el que está sobre y luego debes de sacarle la raíz a la resta y hallas las 2 respuestas usando…