Question

If $a, b$ are roots of quadratic equation $(2-b) x^2+\left(b^2-3 b\right) x+b^2=0 ; b \neq 2 ; b \neq 0$ then

• A. a, b, ab are in A.P.
• B. $ ab , a , b$ are in A.P.
• C. $2^{ ab }, 2^{ a }, 2^{ b }$ are in G.P.
• D. $\frac{1}{a}, \frac{1}{b}, \frac{1}{a b}$ are in H.P.

Answer 1

Answer: (B), (C)

$a b=\frac{b^2}{2-b} \Rightarrow a=\frac{b}{2-b}$
$\therefore a +1=\frac{2}{2- b } \Rightarrow( a +1) b =\frac{2 b }{2- b }=2 a $
$\Rightarrow ab + b =2 a $
$\therefore ab , a , b \text { are in A.P. } $
$\therefore 2^{ ab }, 2^{ a }, 2^{ b } \text { are in G.P. }$