Question

Find the solution set of $x$ which satisfies the inequality $x^2-x-2>0$,

• A. $x>-1$
• B. $x>2$
• C. $x<-1$
• D. $x<-1$ or $x>2$
• E. No solutions are possible

Answer 1

The correct option is D $x<-1$ or $x>2$

$x^2-x-2>0$

$\Rightarrow x^2-2x+x-2>0$

$\Rightarrow x(x-2)+1(x-2)>0$

$\Rightarrow (x+1)(x-2)>0$

$\therefore x<-1$ or $x>2$