Question

If the equations $x^2-4 x+5=0$ and $2 x^2-4[2 a+b] x+b=0(a, b \in R)$ have a common root, then maximum value of $\log _{ b -2}|2 a |$ lies in the interval

• A. $(0,1)$
• B. $(1,2)$
• C. $(0,2)$
• D. $(-1,1)$

Answer 1

Answer: (C)

$\Theta$ Roots of equation $x^2-4 x+5=0$ are imaginary
$\therefore$ Both roots are in common
$\frac{2}{1}=\frac{4[2 a + b ]}{4}=\frac{ b }{5} $
$\Rightarrow b =10 \text { and }[2 a + b ]=2 $
$\Rightarrow[2 a ]=-8 \Rightarrow-8 \leq 2 a <-7 $
$7<|2 a | \leq 8 $
$\text { maximum of } \log _{ b -2}|2 a |=\log _8 8=1 $