Question

2) As raizes da equação x2 - 5 x + 6 =
O são:
1 ponto
O A) 3 e 2
O B) 6 e - 1
OC) - 3 2 - 2
O D) - 3 e 2
O E) 1 e 6​

Answer 1

$\Large\text{\checkmark}$ A) 3 e 2

Cálculo:

$\boxed{\Large\text{\bf{x^2 ~-~5x~+~6~=~0}}}$

$\large\text{\dashrightarrow ~\bf{a}~=~1}\\\\\large\text{\dashrightarrow ~\bf{b}~=~-5}\\\\\large\text{\dashrightarrow ~\bf{c}~=~6}$

$\Large\text{\bf{\Delta ~=~b^2 ~-~4~.~a~.~c}}$

$\large\text{\Delta ~=~b^2 ~-~4~.~a~.~c}\\\\\large\text{\Delta ~=~(-5)^2 ~-~4~.~1~.~6}\\\\\large\text{\Delta ~=~25~-~24}\\\\\large\text{\Delta ~=~1}$

$\Large\text{\bf{x~=~ \dfrac{-b~\pm~\sqrt{\Delta}}{2~.~a} }}$

$\large\text{x~=~ \dfrac{-(-5)~\pm~\sqrt{1}}{2~.~1} }\\\\\\\large\text{x~=~ \dfrac{+~5~\pm~1}{2} }\\\\\\\\\large\text{x_{1} ~=~ \dfrac{+~5~+~1}{2} }\\\\\\\large\text{x_{1} ~=~ \dfrac{+~6}{2} }\\\\\\\boxed{\boxed{\large\text{\bf{x_{1} ~=~+~3}}}}\\\\\\\large\text{x_{2} ~=~ \dfrac{+~5~-~1}{2} }\\\\\\\large\text{x_{2} ~=~ \dfrac{+~4}{2} }\\\\\\\boxed{\boxed{\large\text{\bf{x_{2} ~=~+~2}}}}$