Question

If both roots of the equation $x^2-2ax+a^2-1=0$ lie between $(-2,2)$, then $\left[a\right]$ where $[.]$ stands for greatest integer can be

• A. $-1$
• B. $1$
• C. $2$
• D. $0$

Answer 1

Answer: (A), (D)

The correct options are
A $-1$
D $0$

The given equation $x^2-2ax+a^2-1=0$
$\Rightarrow (x-a{)}^2-1^2=0$
$\Rightarrow (x-a+1)(x-a-1)=0$
$\Rightarrow x=a-1,x=a+1$
Thus, the roots are $a-1$ and $a+1$.
Also, $a+1>a-1$.
For these roots to lie between $-2$ and $2$, we must have
$a-1>-2$ & $a+1<2$
$\Rightarrow a>-1$ & $a<1$
$\Rightarrow -1<a<1$
$\Rightarrow \left[a\right]=-1,0$.