Question

Determine o conjunto solução da equação: x² + 12x - 189 = 0, resolva para professora

Answer 1

Resposta:

Explicação passo-a-passo:

$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}+12x-189=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=12~e~c=-189\\\\\Delta=(b)^{2}-4(a)(c)=(12)^{2}-4(1)(-189)=144-(-756)=900\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(12)-\sqrt{900}}{2(1)}=\frac{-12-30}{2}=\frac{-42}{2}=-21\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(12)+\sqrt{900}}{2(1)}=\frac{-12+30}{2}=\frac{18}{2}=9\\\\S=\{-21,~9\}$