We know the equation x2 + (M + 2) x + 2m-1 = 0 about X. (1) prove that the equation has two unequal real roots. (2) when m is the value, the two roots of the equation are opposite to each other? The solution of the equation is obtained

We know the equation x2 + (M + 2) x + 2m-1 = 0 about X. (1) prove that the equation has two unequal real roots. (2) when m is the value, the two roots of the equation are opposite to each other? The solution of the equation is obtained

(1) It is proved that: △ = (M + 2) 2-4 (2m-1) = m2-4m + 8 = (m-2) 2 + 4, ∵ (m-2) 2 ≥ 0, ∵ (m-2) 2 + 4 ＞ 0, that is △ 0, so the equation has two unequal real roots; (2) let the two roots of the equation be x1, X2, from the meaning of the question: X1 + x2 = 0, that is, M + 2 = 0, the solution is m = - 2, when m = - 2, the two equations are opposite numbers, when m = - 2, the original equation is x2-5 = 0, the solution is X1 = - 5 ，x2=5．