Question

Determinați cea mai mică soluție reală a ecuației 6x^2 + 5x + 1 = 0

Answer 1

$6 {x}^{2} + 5x + 1 = 0$

$a = 6$

$b = 5$

$c = 1$

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

$\Delta = {5}^{2} - 4 \times 6 \times 1$

$\Delta = 25 - 24$

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

$x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}$

$x_{1,2}=\frac{-5\pm\sqrt{1}}{2 \times 6}$

$x_{1,2}=\frac{-5\pm1}{12}$

$x_{1}=\frac{-5 + 1}{12}$

$x_{1}=\frac{ - 4}{12}$

$x_{1}= - \frac{4}{12}$

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

$x_{2}=\frac{-5 - 1}{12}$

$x_{2}=\frac{- 6}{12}$

$x_{2}= - \frac{6}{12}$

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

$x_{2} < x_{1} = > - \frac{1}{2} < - \frac{1}{3}$