• # question_answer Let $f(x)={{x}^{2}}-5x+6,$$g(x)=f(|x|),$$h(x)=|g(x)|$ and $\phi (x)=h(x)-(x)$ are four functions where $(x)$ is the least integral function of $x\ge x$. Then, the number of solutions of the equation, $g(x)=0$ is A)  0                                 B)  2                  C)  4                                 D)  6

Given $g(x)=0$ $\Rightarrow$            $f(|x|)=0$ $\Rightarrow$            ${{x}^{2}}-5|x|+6=0$ $\Rightarrow$            $\left\{ \begin{matrix} {{x}^{2}}-5x+6=0,\,\,x\ge 0 \\ {{x}^{2}}+5x+6=0,\,\,x<0 \\ \end{matrix} \right.$ $\Rightarrow$            $\left\{ \begin{matrix} x=2,\,3,\,\,x\ge 0 \\ x=-3,\,-2,\,\,\,x<0 \\ \end{matrix} \right.$ $\therefore$    Number of solutions = 4