\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfKttLearuGlw5gvP1wzaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFf % euY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9 % q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqaba % WaaqaafaaakqaabeqaaabaaaaaaaaapeGaeGOmaiJaemiEaG3damaa % CaaaleqabaWdbiabikdaYaaakiabgkHiTiabdIha4jabgUcaRiabio % daZiabg2da9iabikdaYiabd2gaTjabgkHiTiabigdaXaqaaiabgsDi % BlabikdaYiabdIha49aadaahaaWcbeqaa8qacqaIYaGmaaGccqGHsi % slcqWG4baEcqGHRaWkcqaIZaWmcqGHsislcqaIYaGmcqWGTbqBcqGH % RaWkcqaIXaqmcqGH9aqpcqaIWaamaeaacqGHuhY2cqaIYaGmcqWG4b % aEpaWaaWbaaSqabeaapeGaeGOmaidaaOGaeyOeI0IaemiEaGNaey4k % aSIaeGinaqJaeyOeI0IaeGOmaiJaemyBa0Maeyypa0JaeGimaadaaa % a!6921! \begin{array}{l} 2{x^2} - x + 3 = 2m - 1\,\,\,\,(1)\\ \Leftrightarrow 2{x^2} - x + 3 - 2m + 1 = 0\\ \Leftrightarrow 2{x^2} - x + 4 - 2m = 0\,\,\,\,\,(2) \end{array}\)

Ta có 

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfKttLearuGlw5gvP1wzaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFf % euY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9 % q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqaba % Waaqaafaaakqaabeaeaaaaaaaaa8qabaGaeyiLdqKaeyypa0JaemOy % ai2aaWbaaSqabeaacqaIYaGmaaGccqGHsislcqaI0aancqWGHbqycq % WGJbWyaeaacqGH9aqpdaqadaqaaiabgkHiTiabigdaXaGaayjkaiaa % wMcaamaaCaaaleqabaGaeGOmaidaaOGaeyOeI0IaeGinaqJaeiOla4 % IaeGOmaiJaeiOla4YaaeWaaeaacqaI0aancqGHsislcqaIYaGmcqWG % TbqBaiaawIcacaGLPaaaaeaacqGH9aqpcqaIXaqmcqGHsislcqaIZa % WmcqaIYaGmcqGHRaWkcqaIXaqmcqaI2aGncqWGTbqBaeaacqGH9aqp % cqaIXaqmcqaI2aGncqWGTbqBcqGHsislcqaIZaWmcqaIXaqmaaaa!6494! \begin{array}{l} \Delta = {b^2} - 4ac\\ = {\left( { - 1} \right)^2} - 4.2.\left( {4 - 2m} \right)\\ = 1 - 32 + 16m\\ = 16m - 31 \end{array}\)

Phương trình (1) vô nghiệm \(\Leftrightarrow\) (2) vô nghiệm

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfKttLearuGlw5gvP1wzaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFf % euY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9 % q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqaba % WaaqaafaaakabaaaaaaaaapeqaaiabgsDiBlabgs5aejabgYda8iab % icdaWiabgsDiBlabigdaXiabiAda2iabd2gaTjabgkHiTiabiodaZi % abigdaXiabgYda8iabicdaWiabgsDiBlabd2gaTjabgYda8maalaaa % baGaeG4mamJaeGymaedabaGaeGymaeJaeGOnaydaaaaa!53DE! \Leftrightarrow \Delta < 0 \Leftrightarrow 16m - 31 < 0 \Leftrightarrow m < \frac{{31}}{{16}}\)