Question

Write the solution set of the equation $x^2+x-2=0$ in roster form.

Answer 1

Determine the solution set of the equation $x^2+x-2=0$ and write in roster form.

$$\begin{gathered} x^2+x-2=0 \\ \Rightarrow x^2+(2-1)x-2=0 \\ \Rightarrow x^2+2x-1x-2=0 \\ \Rightarrow x(x+2)-1(x+2)=0 \\ \Rightarrow (x+2)(x-1)=0 \\ \Rightarrow x+2=0,\mathrm{or}x-1=0 \\ \therefore x=-2,\mathrm{or}x-1=0 \end{gathered}$$

Hence, the solution set of the equation $x^2+x-2=0$ in roster form is $\{1,-2\}$.