12 c va rog e ușor dar am uitat

[tex] {x}^{2} + 2x + 3 = 0[/tex]

[tex]a = 1[/tex]

[tex]b = 2[/tex]

[tex]c = 3[/tex]

[tex]\Delta = {b}^{2} - 4ac[/tex]

[tex]\Delta = {2}^{2} - 4 \times 1 \times 3[/tex]

[tex]\Delta = 4 - 12[/tex]

[tex]\Delta = - 8 < 0 = > \nexists \: x_{1},x_{2}\:\in\:\mathbb{R}[/tex]

[tex] = > \exists \: x_{1}\:\neq\:x_{2}\:\in\:\mathbb{C}[/tex]

[tex]x_{1,2}=\frac{-b\pm\:i\sqrt{-\Delta}}{2a}[/tex]

[tex]x_{1,2}=\frac{-2\pm\:i\sqrt{ - (-8)}}{2 \times 1}[/tex]

[tex]x_{1,2}=\frac{-2\pm\:i\sqrt{8}}{2}[/tex]

[tex]x_{1,2}=\frac{-2\pm\:2 \sqrt{2}i }{2}[/tex]

[tex]x_{1}=\frac{-2 + \:2 \sqrt{2}i }{2}[/tex]

[tex]x_{1}=\frac{2( - 1+ \sqrt{2}i )}{2}[/tex]

[tex]x_{1}= - 1+ \sqrt{2}i [/tex]

[tex]x_{2}=\frac{ - 2-2\sqrt{2}i }{2}[/tex]

[tex]x_{2}=\frac{2( - 1-\sqrt{2}i )}{2}[/tex]

[tex]x_{2}=- 1-\sqrt{2}i [/tex]

x²+2x+3=0
 Δ=b²-4ac  , a=1 b=2 si c=3
Δ=2²-4·1·3 ⇒Δ=4-12 ⇒Δ=-8 ⇒ Δ<0  , deci ecuatia nu are solutii reale deoarece
 Δ <0 , conform teoriei invatate la ecuatia de gradul II.