It is known that the two roots of the equation X2 - (12-m) x + M-1 = 0 about X are positive integers

It is known that the two roots of the equation X2 - (12-m) x + M-1 = 0 about X are positive integers

∵ the two roots of the equation X2 - (12-m) x + M-1 = 0 of X are positive integers, ∵ = b2-4ac ≥ 0, that is [- (12-m)] 2-4 × (m-1) ≥ 0, ∵ (M-14) 2 ≥ 48, the solution is m ≥ 14 + 43 or m ≤ 14-43. Let the two equations be X1 and X2 respectively. According to Weida's theorem, it is obtained that X1 + x2 = 12-m ≥ 0, x1x2 = M-1 > 0, the solution is m ≤ 12 and M > 1. In conclusion, 1 < m ≤ 14-43. ∵ 12-m is an integer, and M-1 Is an integer, M can take 2, 3, 4, 5, 6, 7. To sum up, the value of M can be: 2, 3, 4, 5, 6, 7

It is known that the two roots of the square - (12-m) x + M-1 = 0 of the quadratic equation with one variable X are positive integers, so we can find the value of M

Both are known to be positive integers
So if 12-m > 0 and M-1 > 0, the solution is 1

We know the equation x ^ 2-2 (M + 1) x + m ^ 2 = 0 about X. (1) when m takes what value, the equation has two real roots? (2) choose a suitable integer for M
, so that the equation has two unequal real roots, and find the two roots

(1) if Δ = 4 (M + 1) ^ 2-4m ^ 2 = 8m + 4 ≥ 0, m ≥ - 1 / 2
(2) let m = 0, Δ = 4,
The equation is: x ^ 2-2x = 0
X(X-2)=0
X1=0,X2=2.