Question

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

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

Answer 1

Answer: (C)

x < -1 or x > 3

$a+ar+a{r}^2=x.ar$
or $r^2+r(1-x)+1=0$ (r is real)
$\Delta >0$ i.e. $(1-x{)}^2-4>0$
or, $x^2-2x-3>0$
or, $(x+1)(x-3)>0$
$\Rightarrow x<-1$ or $x>3$