Question

raizes complexas de x2+3x+4

Answer 1

Utilizando Bhaskara, temos:

$\Delta~=~3^2-4.1.4~=~9-16~=~\boxed{-7}\\\\\\\\x'~=~\dfrac{-3+\sqrt{-7}}{2~.~1}~=~\dfrac{-3+\sqrt{-1~.~7}}{2}~=~\dfrac{-3+\sqrt{-1}.\sqrt{7}}{2}~=~\dfrac{-3+i.\sqrt{7}}{2}\\\\\\\boxed{x'~=~-\dfrac{3}{2}~+~i\,\dfrac{\sqrt{7}}{2}}\\\\\\\\x''~=~\dfrac{-3-\sqrt{-7}}{2~.~1}~=~\dfrac{-3-\sqrt{-1~.~7}}{2}~=~\dfrac{-3-\sqrt{-1}.\sqrt{7}}{2}~=~\dfrac{-3-i.\sqrt{7}}{2}\\\\\\\boxed{x''~=~-\dfrac{3}{2}~-~i\,\dfrac{\sqrt{7}}{2}}$

Answer 2

x²+3x+4=0

∆=(3)²-4(1)(4)

∆=9-16

∆=-7

r'= (-3+√-7)/2 = (-3 +7i)/2

r"= (-3-√-7)/2 = (-3 -7i)/2

s={ (-3+7i)/2 , (-3-7i)/2 }