Question

Ache as raízes das equações:
5)x2 -x-20=0
6)x2 -3x-4=0
7)x2 -8x+7=0

Answer 1

Resposta:

Explicação passo a passo:

5)

$\displaystyle Aplicando~a~f\acute{o}rmula~de~Bhaskara~para~x^{2}-x-20=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=1{;}~b=-1~e~c=-20\\\\C\acute{a}lculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(-1)^{2}-4(1)(-20)=1-(-80)=81\\\\C\acute{a}lculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-1)-\sqrt{81}}{2(1)}=\frac{1-9}{2}=\frac{-8}{2}=-4\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-1)+\sqrt{81}}{2(1)}=\frac{1+9}{2}=\frac{10}{2}=5\\\\S=\{-4,~5\}$

6)

$\displaystyle Aplicando~a~f\acute{o}rmula~de~Bhaskara~para~x^{2}-3x-4=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=1{;}~b=-3~e~c=-4\\\\C\acute{a}lculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(-3)^{2}-4(1)(-4)=9-(-16)=25\\\\C\acute{a}lculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-3)-\sqrt{25}}{2(1)}=\frac{3-5}{2}=\frac{-2}{2}=-1\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-3)+\sqrt{25}}{2(1)}=\frac{3+5}{2}=\frac{8}{2}=4\\\\S=\{-1,~4\}$

7)

$\displaystyle Aplicando~a~f\acute{o}rmula~de~Bhaskara~para~x^{2}-8x+7=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=1{;}~b=-8~e~c=7\\\\C\acute{a}lculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(-8)^{2}-4(1)(7)=64-(28)=36\\\\C\acute{a}lculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-8)-\sqrt{36}}{2(1)}=\frac{8-6}{2}=\frac{2}{2}=1\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-8)+\sqrt{36}}{2(1)}=\frac{8+6}{2}=\frac{14}{2}=7\\\\S=\{1,~7\}$