Question

equações do 2° grau completas

A) X²+6x+9=0

B) X²+6x+8=0

C)X²+3x-4=0

D)8x²+2x-1=0

E)X²-2x-8=0​

Answer 1

Resposta:

equações do 2° grau completas

A) X²+6x+9=0

B) X²+6x+8=0

C)X²+3x-4=0

D)8x²+2x-1=0

E)X²-2x-8=

Explicação passo-a-passo:

equações do 2° grau completas

A) X²+6x+9=0

B) X²+6x+8=0

C)X²+3x-4=0

D)8x²+2x-1=0

E)X²-2x-8=

Answer 2

$\large\boxed{\begin{array}{l}\sf A)~\rm x^2+6x+9=0\\\begin{cases}\sf a=1\\\sf b=6\\\sf c=9\end{cases}\\\\\rm\Delta=b^2-4ac\\\rm\Delta=6^2-4\cdot1\cdot9\\\rm\Delta=36-36\\\rm\Delta=0\\\rm x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\rm x=\dfrac{-6\pm\sqrt{0}}{2\cdot1}\\\\\rm x=\dfrac{-6\pm0}{2}\\\\\rm x_1=x_2=\dfrac{-6}{2}=-3\\\rm S=\{-3\}\end{array}}$

$\large\boxed{\begin{array}{l}\sf B)~\rm x^2+6x+8=0\\\begin{cases}\sf a=1\\\sf b=6\\\sf c=8\end{cases}\\\rm\Delta=b^2-4ac\\\rm\Delta=6^2-4\cdot1\cdot8\\\rm\Delta=36-32\\\rm\Delta=4\\\rm x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\rm x=\dfrac{-6\pm\sqrt{4}}{2\cdot1}\\\\\rm x=\dfrac{-6\pm2}{2}\begin{cases}\rm x_1=\dfrac{6+2}{2}=-\dfrac{4}{2}=-2\\\\\rm x_2=\dfrac{-6-2}{2}=-\dfrac{8}{2}=-4 \end{cases}\\\\\rm S=\{-4,-2\}\end{array}}$

$\large\boxed{\begin{array}{l}\sf C)~\rm x^2+3x-4=0\\\rm\Delta=b^2-4ac\\\rm\Delta=3^2-4\cdot1\cdot(-4)\\\rm\Delta=9+16\\\rm\Delta=25\\\\\rm x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\rm x=\dfrac{-3\pm\sqrt{25}}{2\cdot1}\\\\\rm x=\dfrac{-3\pm5}{2}\begin{cases}\rm x_1=\dfrac{-3+5}{2}=\dfrac{2}{2}=1\\\\\rm x_2=\dfrac{-3-5}{2}=-\dfrac{8}{2}=-4 \end{cases}\\\\\rm S=\{-4,1\}\end{array}}$

$\large\boxed{\begin{array}{l}\sf D)~\rm 8x^2+2x-1=0\\\begin{cases}\sf a=8\\\sf b=2\\\sf c=-1\end{cases}\\\rm\Delta=b^2-4ac\\\rm\Delta=2^2-4\cdot8\cdot(-1)\\\rm\Delta=4+32\\\rm\Delta=36\\\rm x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\rm x=\dfrac{-2\pm\sqrt{36}}{2\cdot8}\\\\\rm x=\dfrac{-2\pm6}{16}\begin{cases}\rm x_1=\dfrac{-2+6}{16}=\dfrac{4\div4}{16\div4}=\dfrac{1}{4}\\\\\rm x_2=\dfrac{-2-6}{16}=-\dfrac{8\div8}{16\div8}=-\dfrac{1}{2}\end{cases}\\\\\rm S=\!\bigg\{\!\!-\dfrac{1}{2},\dfrac{1}{4}\bigg\}\end{array}}$

$\large\boxed{\begin{array}{l}\sf E)~\rm x^2-2x-8=0\\\begin{cases}\sf a=~~1\\\sf b=-2\\\sf c=-8\end{cases}\\\rm\Delta=b^2-4ac\\\rm\Delta=(-2)^2-4\cdot1\cdot(-8)\\\rm\Delta=4+32\\\rm\Delta=36\\\rm x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\rm x=\dfrac{-(-2)\pm\sqrt{36}}{2\cdot1}\\\\\rm x=\dfrac{2\pm6}{2}\begin{cases}\rm x_1=\dfrac{2+6}{2}=\dfrac{8}{2}=4\\\\\rm x_2=\dfrac{2-6}{2}=-\dfrac{4}{2}=-2\end{cases}\\\\\rm S=\{-2,4\}\end{array}}$