Question

Calcular las rayces de f(x)=x^2-4x+3

Answer 1

SOLUCIÓN

♛ HØlα!! ✌

Para hallar las raíces hacemos que f(x) = 0,entonces

                         $Sea\:la\:ecuaci\'on\:cuadr\'atica:\\\\\\ax^2+bx+c=0\\\\\\Por\:f\'ormula\:general\:tenemos\:que:\\\\\\\mathrm{\boxed{x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}}\\\\\\Del\:problema:\\\\\\a=1,b=-4,c=3\\\\\\ Entonces\:reemplazamos\\\\\\x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x_{1,2}=\dfrac{-(-4)\pm \sqrt{(-4)^2-[4(1)(3)]}}{2(1)}\\\\\\x_{1,2}=\dfrac{4\pm \sqrt{16-(12)}}{2}\\\\\\x_{1,2}=\dfrac{4\pm \sqrt{4}}{2}\\\\\\x_{1,2}=\dfrac{4\pm2}{2}$

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

Rpta. Las raíces serán 1 y 3