Question

Розв’язати нерівність: 2х² +5х – 3 ≤ 0.​

Answer 1

$2 {x}^{2} + 5x - 3 = 0 \\ a = 2 \\ b =5  \\ c = - 3  \\ D =  {b}^{2}  - 4ac = {5}^{2} - 4 \times 2 \times ( - 3) = 25 + 24 = 49 \\ x_{1} = \frac{ - 5 - 7}{2 \times 2} = - \frac{12}{4} = - 3 \\ x_{2} = \frac{ - 5 + 7}{2 \times2 } = - \frac{2}{4} = 0.5 \\ \\ 2 {x}^{2} + 5x - 3 \leqslant 0 \\ (x + 3)(x - 0.5) \leqslant 0 \\ + + + + [ - 3] - - - - [0.5] + + + + \\ x \: \in\: [ - 3; \: 0.5]$