Question

Usando Bhaskara, calcule as raízes de x² - x - 20 = 0. *

Answer 1

Resposta:

Explicação passo-a-passo:

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-x-20=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-1~e~c=-20\\\\\Delta=(b)^{2}-4(a)(c)=(-1)^{2}-4(1)(-20)=1-(-80)=81\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-1)-\sqrt{81}}{2(1)}=\frac{1-9}{2}=\frac{-8}{2}=-4\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-1)+\sqrt{81}}{2(1)}=\frac{1+9}{2}=\frac{10}{2}=5\\\\S=\{-4,~5\}$