Question

Three distinct real numbers, a, b, c are in G.P. such that a + b+ c= x b, then

• A. x<-1 or x>3
• B. 0<x<1
• C. -1<x<2
• D. -1<x<3

Answer 1

The correct option is A

x<-1 or x>3

a + ar + a$r^2$ = x. ar

or, $r^2$ + r (1-x) + 1 = 0, r is real

∆>0 i.e.${(1-x)}^2$- 4 >0

Or,$x^2$-2x-3>0

Or, (x+1) (x-3)>0

⇒ x<-1 or x>3