X² + 10x + 21 = 0
formula general

Respuestas

Respuesta dada por: roycroos

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

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

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

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

╚═════════════════════════════════════════════╝

En el problema

$\mathsf{\underbrace{\boldsymbol{1}}_{a}x^2\:+\:\underbrace{\boldsymbol{10}}_{b}x\:+\:\underbrace{\boldsymbol{21}}_{c}=0}$

Entonces a = 1, b = 10, c = 21

Reemplazamos los coeficientes en la fórmula general:

$\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-(10) \pm \sqrt{(10)^2 - [4(1)(21)]}}{2(1)}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-10 \pm \sqrt{100 - (84)}}{2}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-10 \pm \sqrt{16}}{2}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-10 \pm 4}{2}}$

$\center \Rightarrow\:\mathrm{x_{1}} \mathrm{= \dfrac{-10 + 4}{2}}\\\\\\\center \mathrm{x_{1}} \mathrm{= \dfrac{-6}{2}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{1}} \mathrm{= -3}}}}$ $\center \Rightarrow\:\mathrm{x_{2}} \mathrm{= \dfrac{-10 - 4}{2}}\\\\\\\center \mathrm{x_{2}} \mathrm{= \dfrac{-14}{2}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{2}} \mathrm{= -7}}}}$