How to judge the positive and negative of the root of an equation by Weida's theorem

How to judge the positive and negative of the root of an equation by Weida's theorem

If C / A is positive, the sign is the same
On the contrary
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The extended practice of Veda's theorem
It is known that the two roots of the equation x & # 178; - (12-m) x + M-1 = 0 about X are positive integers, so we can find the value of M

7 is 2,3

The extended exercises of Weida theorem
Find the real number k such that the roots of the equation x & # 178; + (K + 1) x + (k-1) = 0 are integers
Please write the process, thank you

The sum of the two is - (K + 1), and the product of the two is k-1
Because the roots are integers, so - (K + 1), k-1 are integers
So K is also an integer
The deformation of the equation is X & # 178; + X-1 + K (x + 1) = 0
Because the equation x = - 1 is not true, we can get k from it
k=(-x²-x+1)/(x+1)=-x+ 1/(x+1)
Since K and X are integers, (x + 1) must be a divisor of 1
Then x + 1 = 1 or - 1
When x + 1 = 1, x = 0, k = 1
When x + 1 = - 1, x = - 2, k = 1
So let the roots of the equation be all integers, k = 1