Question

Determine as raízes da função quadrática : y = x² - 4x - 5

Answer 1

Resposta:

Explicação passo-a-passo:

Para achar a raiz da função faça y=0

$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-4x-5=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-4~e~c=-5\\\\\Delta=(b)^{2}-4(a)(c)=(-4)^{2}-4(1)(-5)=16-(-20)=36\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-4)-\sqrt{36}}{2(1)}=\frac{4-6}{2}=\frac{-2}{2}=-1\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-4)+\sqrt{36}}{2(1)}=\frac{4+6}{2}=\frac{10}{2}=5\\\\S=\{-1,~5\}$