Question

Calcule o discriminante e indique as raízes da equação x² + 5x + 6=0.​

Answer 1

Resposta:

O discriminante Δ=1.

S={-3,-2}

Explicação passo-a-passo:

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}+5x+6=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=5~e~c=6\\\\\Delta=(b)^{2}-4(a)(c)=(5)^{2}-4(1)(6)=25-(24)=1\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(5)-\sqrt{1}}{2(1)}=\frac{-5-1}{2}=\frac{-6}{2}=-3\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(5)+\sqrt{1}}{2(1)}=\frac{-5+1}{2}=\frac{-4}{2}=-2\\\\S=\{-3,~-2\}$