Verified answer

Нет корней при D<0:

[tex]2 {x}^{2} + mx + 1 = 0 \\ a =2 \\ b =m \\ c = 1\\ D = {b}^{2} - 4ac = {m}^{2} - 4 \times 2 \times 1 = m {}^{2} - 8 \\ m {}^{2} - 8 < 0 \\ (m - \sqrt{8} )(m + \sqrt{8} ) < 0 \\ (m - 2 \sqrt{2} )(m + 2 \sqrt{2} ) < 0 \\ + + + + + ( - 2 \sqrt{2} ) - - - - - (2 \sqrt{2} ) + + + + + \\m \: \epsilon \: ( - 2 \sqrt{2} ; \: 2 \sqrt{2} )[/tex]