Question

Quais são as raízes da equação x² - 14x + 48 = 0? *

a) S = { 6, 8 }

b) S = {4 e 8}

c) S = {9 e 10}

d) S = { 1, 5 }

e) S = { -6, -4}

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Answer 1

Resposta:

Alternativa a)

Explicação passo-a-passo:

$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-14x+48=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-14~e~c=48\\\\\Delta=(b)^{2}-4(a)(c)=(-14)^{2}-4(1)(48)=196-(192)=4\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-14)-\sqrt{4}}{2(1)}=\frac{14-2}{2}=\frac{12}{2}=6\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-14)+\sqrt{4}}{2(1)}=\frac{14+2}{2}=\frac{16}{2}=8\\\\S=\{6,~8\}$