Question

Quais são as raizes da expressão 9x2+9X+2=0

Answer 1

$9 x^{2} +9x+2=0\\\\ a=1~;~b=9~;~c=2\\\\\\ \Delta=b^2-4ac\to \Delta=9^2-4.9.2\to \Delta=81-72\to \boxed{\Delta=9}\\\\ x' \neq x''\\\\\\ x= \dfrac{-b\pm \sqrt{\Delta} }{2a} \to~~ x= \dfrac{-9\pm \sqrt{9} }{2.9} \to~~ x= \dfrac{-9\pm 3 }{18} \to\\\\ x'= \dfrac{-9+ 3 }{18} \to~~x'= \dfrac{-6 }{18} \to~~ \boxed{x'= -\dfrac{1 }{3} } \\\\\\ x'= \dfrac{-9- 3 }{18} \to~~x'= \dfrac{-12 }{18} \to~~ \boxed{x'= -\dfrac{2 }{3} } \\\\\\\\ \boxed{ S=\left\{-\dfrac{2 }{3} ~;~-\dfrac{1 }{3}\right\}}$