Question

A raiz da equação 6x² + x - 1 = 0 é

Answer 1

6x² + x - 1 = 0 

Δ = 1 + 4.6 

Δ = 1 + 24 

Δ = 25 


x = -1 +-√25/12 
x = -1 +-5/12

x' = -1+5/12
x' = 4/12
x' = 1/3 

x'' = -1-5/12
x'' = -6/12
x'' = -1/2                           S = { -1/2 , 1/3 }                               ok

Answer 2

Equação do 2° grau

$6 {x}^{2} +x - 1 = 0 \\ \\ a = 6 \\ b = 1 \\ c = ( - 1) \\ \\ \Delta = {b}^{2} - 4ac \\ \Delta = {1}^{2} - 4 \cdot6 \cdot( - 1) \\\Delta = 1 - 24 \cdot( - 1) \\ \Delta = 1 + 24 \\ \Delta = 25 \\ \\ x = \frac{ - b\pm \sqrt{\Delta} }{2a} \\ \\ x = \frac{ - 1\pm \sqrt{25} }{2 \cdot6 } \\ \\ x = \frac{ - 1\pm 5 }{12} \\ \\ x_{1} = \frac{ - 1 + 5}{12} = \frac{ {4}^{\color{red} { \div 4}} }{ {12}^{\color{red} { \div 4}} } = \bf{ \frac{1}{3} } \\ \\ x_{2} = \frac{ - 1 - 5}{12} = - \frac{ {6}^{\color{red} { \div 6}} }{ {12}^{\color{red} { \div 6}} } = - \bf{ \frac{1}{2} }$

$\boxed{ \bf{S = \{ - \frac{1}{2} , \: \frac{1}{3} \} } }$ <--- Raízes