Question

2x^2 + 2x + 3 =0

5m^2 + 2m =0

36w- w^2 =62

(me ayudarían con la formula general por favor)

Answer 1

Respuesta:

Explicación paso a paso:

2x²+2x+3=0

$a=2\,\,b=2\,\,c=3\\\\x=\frac{-2\pm\sqrt{(2)^{2}-4(2)(3)}}{2(2)}\\\\x=\frac{-2\pm\sqrt{4-24}}{4}\\\\x=\frac{-2\pm\sqrt{-20}}{4}\\\\x=\frac{-2\pm2\sqrt{5}i}{4}=-\frac{1\pm\sqrt{5}i}{2}\\\\x_{1}=-\frac{1}{2}+\frac{\sqrt{5}i}{2}\\\\x_{2}=-\frac{1}{2}-\frac{\sqrt{5}i}{2}$

5m²+2m=0

$a=5\,\,,b=2\,\,,c=0\\\\m=\frac{-2\pm\sqrt{(2)^{2}-4(5)(0)}}{2(5)}\\\\m=\frac{-2\pm\sqrt{4}}{10}\\\\m=\frac{-2\pm2}{10}=\frac{-1\pm1}{5}\\\\m_{1}=-\frac{1}{5}+\frac{1}{5}=0\\\\m_{2}=-\frac{1}{5}-\frac{1}{5}=-\frac{2}{5}$

-w²+32w=62

-w²+32w-62=0

$a=-1\,\,,b=32\,\,,c=-62\\\\w=\frac{-32\pm\sqrt{(32)^{2}-4(-1)(-62)}}{2(-1)}\\\\w=\frac{-32\pm\sqrt{1024-248}}{-2}\\\\w=\frac{-32\pm\sqrt{776}}{-2}=\frac{-32\pm2\sqrt{194}}{-2}\\\\w=16\pm(-\sqrt{194})}\\\\w_{1}=16-\sqrt{194}\\\\w_{2}=16+\sqrt{194}$

Saludos.