Question

Como posso resolver este problema?

Uma das raizes da equação x2-6x+34=0

a) 3+5i c)3+2i
b)5+2i d)2+3i

Answer 1

$x^2-6x+34=0\\\\ a=1~;~b=-6~;~c=34\\\\\\ \Delta=b^2-4ac\to \Delta=(-6)^2-4.1.34\to \Delta=36-136\to~~ \boxed{\Delta=-100}\\\\\\\\\\\\ \large\boxed{\sqrt{-1}=i} \\\\ \sqrt{-100} \to~~ \sqrt{-1*100} \to~~ \sqrt{-1}*\sqrt{100} \to~~ i*10\to~~ \boxed{\boxed{10i}}$




$x= \dfrac{-b \pm \sqrt{\Delta} }{2a} \to~~ x= \dfrac{-(-6) \pm \sqrt{-100} }{2.1} \to~~ x= \dfrac{6 \pm 10i }{2} \to\\\\\\ x'= \dfrac{6+ 10i }{2} \to~~\large\boxed{ x'= 3+ 5i }\\\\\\ x''= \dfrac{6- 10i }{2} \to~~\large\boxed{ x''= 3-5i }\\\\\\\\\\ \Large\boxed{\boxed{S=\{ 3-5i~;~3-5i\}} } \\\\\\\\\\\\\ Resposta \to~~~ Letra~~~a) ~3+5i$