a) [tex]2 z^{2} +6z+z+3-5z+10-z ^{2} +1=0[/tex]
[tex] z^{2} +2z+14=0[/tex]
Δ[tex]= b^{2} -4ac= 2^{2} -4*14=4-56=-52[/tex]
[tex] z_{1} = \frac{-b-i \sqrt{-delta} }{2a} = \frac{-4-i \sqrt{52} }{2} = \frac{-4-2i \sqrt{13} }{2} = \frac{2(-2-i \sqrt{13}) }{2} =-2-i \sqrt{13} [/tex]
[tex] z_{2} = \frac{-b+i \sqrt{-delta} }{2a} = \frac{-4+i \sqrt{52} }{2} = \frac{-4+2i \sqrt{13} }{2} = \frac{2(-2+i \sqrt{13}) }{2} =-2+i \sqrt{13} [/tex]
S={[tex]-2-i \sqrt{13} [/tex];[tex]-2+i \sqrt{13} [/tex]}
b)[tex]2 z^{2} +7z+14z+49+ z^{2} -z+7=0[/tex]
[tex]3 z^{2} +20z+56=0[/tex]
Δ[tex]= b^{2} -4ac= 20^{2} -4*3*56=400-672=-272[/tex]
[tex] z_{1} = \frac{-b-i \sqrt{-delta} }{2a} = \frac{-20-i \sqrt{272} }{6}= \frac{-20-4i \sqrt{17} }{6} = \frac{2(-10-2i \sqrt{17}) }{6} =[/tex][tex] \frac{-10-2i \sqrt{17} }{3} [/tex]
[tex] z_{1} = \frac{-b+i \sqrt{-delta} }{2a} = \frac{-20+i \sqrt{272} }{6}= \frac{-20+4i \sqrt{17} }{6} = \frac{2(-10+2i \sqrt{17}) }{6} =[/tex][tex] \frac{-10+2i \sqrt{17} }{3} [/tex]
S={[tex] \frac{-10-2i \sqrt{17} }{3} [/tex];[tex] \frac{-10+2i \sqrt{17} }{3} [/tex]}
