Question

4) Determine as raízes desta equação usando a fórmula de resolução.
$2{x}^{2} + x - 10 = 0$
+ x - 10 = 0​

Answer 1

Resposta:

Explicação passo-a-passo:

2x²+x-10=0$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~2x^{2}+x-10=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=2{;}~b=1~e~c=-10\\\\C\'alculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(1)^{2}-4(2)(-10)=1-(-80)=81\\\\C\'alculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(1)-\sqrt{81}}{2(2)}=\frac{-1-9}{4}=\frac{-10}{4}=-2,5\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(1)+\sqrt{81}}{2(2)}=\frac{-1+9}{4}=\frac{8}{4}=2\\\\S=\{-2,5;~2\}$

x-10=0

x=10

S={10}