Question

Number of integral values of $x$ satisfying ${[x^2-2]}^2-9[x^2-2]+14=0$, where [.] is greatest integer function

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

${[x^2-2]}^2-9[x^2-2]+14=0$

$\text{Let}[x^2-2]=m$

$m^2-9m+14=0$

$\Rightarrow m^2-7m-2m+14=0$

$\Rightarrow m(m-7)-2(m-7)=0$

$\Rightarrow (m-7)(m-2)=0$

$m=7\text{or}m=2$

$[x^2-2]=7\text{or}[x^2-2]=2$

$\text{Possible integral values of}x\text{are:}3\text{,}2$

$\text{Answer: option (B).}$