Question

5) Resolva a equação do 2º grau 2x2 + x-3= 0.

Answer 1

Resposta:

S={x= -3/2, x=1}

Explicação passo a passo:

$\displaystyle Aplicando~a~f\acute{o}rmula~de~Bhaskara~para~2x^{2}+x-3=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=2{;}~b=1~e~c=-3\\\\C\acute{a}lculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(1)^{2}-4(2)(-3)=1-(-24)=25\\\\C\acute{a}lculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(1)-\sqrt{25}}{2(2)}=\frac{-1-5}{4}=\frac{-6}{4}=\frac{-6\div2}{4\div2}=-\frac{3}{2}$

$\displaystyle x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(1)+\sqrt{25}}{2(2)}=\frac{-1+5}{4}=\frac{4}{4}=1$