Question

Resolva: 2z² - 5z - 3 = 0

Answer 1

$\mathtt{2z^2 -5z - 3 = 0} \\ \\ \mathtt{a = 2} \\ \mathtt{b=-5} \\ \mathtt{c=-3} \\ \\ \mathtt{\Delta = b^2-4~.~a~.~c} \\ \\ \mathtt{\Delta = (-5)^2-4~.~2~.~(-3)} \\ \mathtt{\Delta= 25 -8~.~(-3) } \\ \mathtt{\Delta = 25 + 24} \\ \mathtt{\Delta = 49} \\ \\ \\ \mathtt{\frac{-b+-\sqrt{\Delta}}{2~.~a}}$

$\mathtt{\frac{-(-5) +-\sqrt{49}}{2~.~2}} \\ \\ \mathtt{\frac{5 +- 7}{4}} \\ \\ \mathtt{x' = \frac{5 + 7}{4}} \\ \\ \mathtt{x' = \frac{12}{4}} \\ \\ \mathtt{x'= 3} \\ \\ \\ \mathtt{x''= \frac{5 -7}{4}} \\ \\\mathtt{x'' = -\frac{2}{4}} ~~~~~~(\div 2) \\ \\ \mathtt{x'' = - \frac{1}{2}} \\ \\ \\ \boxed{\boxed{\mathtt{Resposta : -\frac{1}{2} ~~~e~~~~~3}}}$