Question

Determine as raízes das funções abaixo:

A) f(x)=2x^2-6x-8

B) g(x)=x^2-15x+50

Answer 1

Explicação passo-a-passo:

$\textrm{F\'ormula geral: } x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\a) \ 2x^2-6x-8=0\\\\\Rightarrow x=\dfrac{-(-6)\pm\sqrt{(-6)^2-4.2.(-8)}}{2.2}\\\\\Rightarrow x=\dfrac{6\pm\sqrt{36+64}}{4}\\\\\Rightarrow x=\dfrac{6\pm\sqrt{100}}{4}\\\\\Rightarrow x=\dfrac{6\pm10}{4}\\\\\Rightarrow x_1=\dfrac{6+10}{4} \ \textrm{ e }\ x_2=\dfrac{6-10}{4} \\\\\\\Rightarrow x_1=\dfrac{16}{4} \ \textrm{ e }\ x_2=\dfrac{-4}{4} \\\\\\\Rightarrow x_1=4 \ \textrm{ e }\ x_2=-1$

$b) \ x^2-15x+50=0\\\\\Rightarrow x=\dfrac{-(-15)\pm\sqrt{(-15)^2-4.1.50}}{2.1}\\\\\\\Rightarrow x=\dfrac{15\pm\sqrt{225-200}}{2}\\\\\\\Rightarrow x=\dfrac{15\pm\sqrt{25}}{2}\\\\\\\Rightarrow x=\dfrac{15\pm5}{2}\\\\\\\\\\\Rightarrow x_1=\dfrac{15+5}{2} \ \textrm{ e }\ x_2=\dfrac{15-5}{2} \\\\\\\Rightarrow x_1=\dfrac{20}{2} \ \textrm{ e }\ x_2=\dfrac{10}{2} \\\\\\\Rightarrow x_1=10 \ \textrm{ e }\ x_2=5$

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