Proof: the equation x2 + MX + 1 = 0 of X has two negative real roots if and only if M ≥ 2

Proof: the equation x2 + MX + 1 = 0 of X has two negative real roots if and only if M ≥ 2

The following results are proved: (1) sufficiency: ∵ m ≥ 2, ∵ (?) = M2-4 ≥ 0, the equation x2 + MX + 1 = 0 has real roots. Let two of x2 + MX + 1 = 0 be x1, x2. According to Weida's theorem, ∵ X1 + x2 = - M ≤ - 2, ∵ x1, X2 are both negative roots