It is known that the equation MX2 - (2m-1) x + M = 0 has two unequal real roots. (1) find the value range of M; (2) find the two roots of the equation when m is the largest integer

It is known that the equation MX2 - (2m-1) x + M = 0 has two unequal real roots. (1) find the value range of M; (2) find the two roots of the equation when m is the largest integer

(1) ∵ the equation MX2 - (2m-1) x + M = 0 has two unequal real roots. The solution of the equation is m ＜ 14 and m ≠ 0 if it is 1-4m ＞ 0 and m ≠ 0; (2) from (1), we know that m ＜ 14 and m ≠ 0, the largest integer of M is - 1, and the equation is: - x2 + 3x-1 = 0, that is, x2-3x + 1 = 0, and the solution is x = - 3 ± 52, ∵ X1 = - 3 + 52, X2 = 3 − 52