Question

1) Resolva as equações do 2° grau e biquadrada: a) 2x² + x – 3 = 0.

Answer 1

Resposta:

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\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\\\\S=\{-\frac{3}{2},~1\}$