Question

3x2-2x+5 formula de bhaskara

Answer 1

$3x^2-2x+5=0\\\\a=3\ \ \ \ \ \ \ \ \ b=-2\ \ \ \ \ \ \ \ \ c=5\\\\\Delta=b^2-4ac\\\Delta=(-2)^2-4\cdot(3)\cdot(5)\\\Delta=4-60\\\Delta=-56\\\\N\~ao\ existe\ solu\c{c}\~ao\ dentro\ do\ Conjunto\ dos\ n\'umeros\ Reais\\\\S=\{\ \}\\\\Resolvendo\ em\ N\'umeros\ Complexos\\\\x=\dfrac{-b \frac{+}{-}\sqrt{\Delta}}{2a}\\\\\\x= \dfrac{-(-2) \frac{+}{-} \sqrt{-56}}{2\cdot3}\\\\\\x= \dfrac{2 \frac{+}{-} \sqrt{-56}}{6}$

$i^2=-1\\\\x= \dfrac{2 \frac{+}{-} \sqrt{56\cdot{i^2}}}{6}\\\\\\x'= \dfrac{2+2 \sqrt{14}i }{6}\\\\\\x'= \dfrac{1}{3}+ \dfrac{ \sqrt{14}}{3}i\\\\\\x"= \dfrac{2- \sqrt{14}i }{6}\\\\\\x"= \dfrac{1}{3}- \dfrac{ \sqrt{14} }{3}i$

$\boxed{S=\bigg\{x\in\mathbb{C}/x= \dfrac{1}{3}+ \dfrac{ \sqrt{14}}{3}i\ ou\ x=\ \dfrac{1}{3}- \dfrac{ \sqrt{14}}{3}i \bigg\}}$