Question

Mulțimea soluțiilor ecuației 2x²+3x+1=0 este ..............

Answer 1

2x²+3x+1=0 
Δ = b² - 4ac = 9 - 4×2×1 = 9 - 8 = 1 
x1 = (-3 + 1)/4 = - 2/4 = - 1/2 
x2 = (-3 - 1)/4 = -4/4 = - 1 

S = {-1/2: - 1 } 

Answer 2

$2 {x}^{2} + 3x + 1 = 0$

$a = 2$

$b = 3$

$c = 1$

$\Delta = {b}^{2} - 4ac$

$\Delta = {3}^{2} - 4 \times 2 \times 1$

$\Delta = 9 - 8$

$\Delta = 1 > 0 = > \exists \: x_{1}\:\neq\:x_{2} \: \in \: \mathbb{R}$

$x_{1,2}=\frac{-3\pm\sqrt{1}}{2 \times 2} = \frac{ - 3 \pm1}{4}$

$x_{1}=\frac{-3 + 1}{4} = - \frac{2}{4} = - \frac{1}{2}$

$x_{2}=\frac{-3 - 1}{4} = - \frac{4}{4} = - 1$

$= > S = \left \{ - \frac{1}{2} , - 1 \right \}$