Mathematics - Quadratic Equation Question with Solution | TestHub

Case I : $x\ge -5$ $\begin{array}{rl}& x^2+5x+2x+12=0\\ & x^2+7x+12=0\\ & x=-3,-4\end{array}$ Case II : $-7<\mathrm{x}<-5$ $-x^2-5x+2x+14-2=0$ $\begin{array}{rl}& -x^2-3x+12=0\\ & x=\frac{-3\pm \sqrt{9+48}}{2}\\ & =\frac{-3\pm \sqrt{57}}{2}\\ & x=\frac{-3-\sqrt{57}}{2},\frac{-3+\sqrt{57}}{2}\text{ (rejected) }\end{array}$ Case III : $\mathrm{x}\le -7$ $\begin{array}{rl}& -x^2-5x-2x-14-2=0\\ & x^2+7x+16=0\\ & D=49-64<0\end{array}$ No solutions No. of solutions $=3$