Question

gente pelo amor de deus me ajuda eu sou muito burra

equaçoes do segundo grau
a) 4x2 - 12x + 5=0 S={ 1/2 , 5/2 }
b) 9y2 - 3y -2=0 S={ - 1/3, 2/3 }
c) 2n2 + 7n + 6=0 S={ -2 , - 3/2}
d) 3x2 + 8x -3=0 S={ -3 , 1/3 }

Answer 1

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$\tt a)~\sf 4x^2-12x+5=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-12)^2-4\cdot4\cdot5\\\sf\Delta=144-80\\\sf\Delta=64\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf x=\dfrac{-(-12)\pm\sqrt{64}}{2\cdot4}\\\sf x=\dfrac{12\pm8}{8}\begin{cases}\sf x_1=\dfrac{12+8}{8}=\dfrac{20}{8}=\dfrac{5}{4}\\\sf x_2=\dfrac{12-8}{8}=\dfrac{4}{8}=\dfrac{1}{2}\end{cases}$

$\tt b)~\sf9y^2-3y-2=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-3)^2-4\cdot9\cdot(-2)\\\sf\Delta=9+72\\\sf\Delta=81\\\sf y=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf y=\dfrac{-(-3)\pm\sqrt{81}}{2\cdot9}\\\sf y=\dfrac{3\pm9}{18}\begin{cases}\sf x_1=\dfrac{3+9}{18}=\dfrac{12}{18}=\dfrac{2}{3}\\\sf x_2=\dfrac{3-9}{18}=-\dfrac{6}{18}=-\dfrac{1}{3}\end{cases}$

$\tt c)~\sf2n^2+7n+6=0\\\sf\Delta=b^2-4ac\\\sf\Delta=7^2-4\cdot2\cdot6\\\sf\Delta=49-48\\\sf\Delta=1\\\sf n=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf n=\dfrac{-(7)\pm\sqrt{1}}{2\cdot2}\\\sf n=\dfrac{-7\pm1}{4}\begin{cases}\sf n_1=\dfrac{-7+1}{4}=-\dfrac{6}{4}=-\dfrac{3}{2}\\\sf n_2=\dfrac{-7-1}{4}=-\dfrac{8}{4}=-2\end{cases}$

$\tt d)~\sf 3x^2+8x-3=0\\\sf\Delta=b^2-4ac\\\sf\Delta=8^2-4\cdot3\cdot(-3)\\\sf\Delta=64+36\\\sf\Delta=100\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf x=\dfrac{-8\pm\sqrt{100}}{2\cdot3}\\\sf x=\dfrac{-8\pm10}{6}\begin{cases}\sf x_1=\dfrac{-8+10}{6}=\dfrac{2}{6}=\dfrac{1}{3}\\\sf x_2=\dfrac{-8-10}{6}=-\dfrac{18}{6}=-3\end{cases}$