Mathematics - Functions Question with Solution | TestHub

Case-1 $\begin{array}{rl}& x\ge 0\\ & x^2+2x-5x-5-1=0\\ & x^2-3x-6=0\\ & x=\frac{3\pm \sqrt{9+24}}{2}=\frac{3\pm \sqrt{33}}{2}\end{array}$ One positive root Case-2 $\begin{array}{rl}& -1\le x<0\\ & -x^2-2x-5x-5-1=0\\ & x^2+7x+6=0\\ & (x+6)(x+1)=0\\ & x=-1\end{array}$ one root in range Case-3 $\begin{array}{rl}& -2\le x<-1\\ & x^2-2x+5x+5-1=0\\ & x^2-3x-4=0\\ & (x-4)(x+1)=0\end{array}$ No root in range Case-4 $\begin{array}{rl}& x<-2\\ & x^2+7x+4=0\\ & x=\frac{-7\pm \sqrt{49-16}}{2}=\frac{7\pm \sqrt{33}}{2}\end{array}$ one root in range Total number of distinct roots are 3