Question

решите квадратное неравенство 4x^2+5x-6<0

Answer 1

4х^2 + 5x - 6 < 0
y = 4х^2 + 5x - 6
4х^2 + 5x - 6 = 0
D = 25 + 96 = 121
$\sqrt{D} = \sqrt{121} = 11$
x₁ = $\frac{-5 + 11}{8} = \frac{6}{8} = \frac{3}{4} = 0,75$
х₂ = $\frac{-5 - 11}{8} = \frac{-16}{8} = -2$
------- -2 --------- 0,75-------->> 
Ветви вверх (↑), т.к. 4х^2 > 0
Ответ: ( -2; 0,75) 

Answer 2

$4 x^{2} +5x-6\ \textless \ 0\\4 x^{2} +5x-6=0\\D=25+96=121 \\ \sqrt{D} =11\\ x_{1} = \frac{-5+11}{8} = \frac{6}{8} = \frac{3}{4} =0.75 \\ \\ x_{2} = \frac{-5-11}{8} =-2$

х ∈$(-2;0.75)$