Question

方程f（x）=ax*2+bx+c=0（a>0）的两个根都大于1的充要条件

Answer 1

设两根是x1,x2,两根都大于1,那么有：

b^2-4ac>=0 (i)

（x1-1)(x2-1)>0 (ii)

x1+x2>2 (iii)

又x1x2=c/a>1>0

=>c>0

(ii)=>x1x2-(x1+x2)+1>0

=>c/a+b/a+1>0

=>a+b+c>a

=>b+c>0

=>b>-c

(iii)=>-b/a>2

=