Asignatura: Matemáticas
Autor: alejandragarcia20080
hace 4 años

x^(2)+5x+6

RESOLVER USANDO FORMULA CUADRATICA

Respuestas

Respuesta dada por: roycroos

╔═════════════════════════════════════════════╗ $\center \mathrm{Una ecuaci\'on cuadr\'atica de la forma:}$

$\mathrm{ax^2 + bx + c=0\:\:donde\:\: a \neq 0}$

$\center \mathrm{Poseer\'a 2 soluciones x_1} \:\mathrm{y\:x_2,\:las\:cuales\:determinaremos\:por:}$

$\boldsymbol{{\mathrm{x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}}} \Rightarrow \boxed{\mathrm{F\'ormula\:general}}$ ╚═════════════════════════════════════════════╝

Reemplazamos los coeficientes en la fórmula general:

$\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-(5) \pm \sqrt{(5)^2 - [4(1)(6)]}}{2(1)}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-5 \pm \sqrt{25 - (24)}}{2}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-5 \pm \sqrt{1}}{2}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-5 \pm 1}{2}}$

$\center \Rightarrow\:\mathrm{x_{1}} \mathrm{= \dfrac{-5 + 1}{2}}\\\\\\\center \mathrm{x_{1}} \mathrm{= \dfrac{-4}{2}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{1}} \mathrm{= -2}}}}$ $\center \Rightarrow\:\mathrm{x_{2}} \mathrm{= \dfrac{-5 - 1}{2}}\\\\\\\center \mathrm{x_{2}} \mathrm{= \dfrac{-6}{2}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{2}} \mathrm{= -3}}}}$