Question

Determine os zeros da funcao f(×)=-ײ+12×+20

Answer 1

Resposta:

Explicação passo-a-passo:

$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~-1x^{2}+12x+20=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=-1{;}~b=12~e~c=20\\\\C\'alculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(12)^{2}-4(-1)(20)=144-(-80)=224\\\sqrt{\Delta}=\sqrt{224}=\sqrt{2^4.14}=4\sqrt{14}$$\displaystyle \\C\'alculo~das~raizes:\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(12)-4\sqrt{14}}{2(-1)}=\frac{-12-4\sqrt{14}}{-2}=6+2\sqrt{14}\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(12)+4\sqrt{14}}{2(-1)}=\frac{-12+4\sqrt{14}}{-2}=6-2\sqrt{14}\\\\\\S=\{6-2\sqrt{14},~6+2\sqrt{14}\}$