Question

等差数列｛an｝中已知公差d不等于0,an不等于0,设方程

Answer 1

∵{an}是等差数列,∴2a(r+1)=a(r)+a(r+2),即a(r)- 2a(r+1)+a(r+2)=0

故当x=-1时,a(r)x^2+2a(r+1)x+a(r+2)

= a(r)- 2a(r+1)+a(r+2)=0

∴当r取不同自然数时,原方程有一个公共根－1