Solve: $x ^ { 2 } - x - 2

Question

Solve: $x ^ { 2 } - x - 2 < 0$
A) $( - \infty , - 1 ) \cup ( 2 , \infty )$
B) $( - \infty , - 1 )$
C) $( - 2,1 )$
D) $( - 1,2 )$

Quizplus · Accepted Answer

To solve the inequality $x^2 - x - 2 < 0$, first factor the quadratic expression. It factors as $(x - 2)(x + 1) < 0$. The roots are $x = 2$ and $x = -1$. The sign of the expression changes at these roots. Testing intervals between and outside these roots, we find that the expression is negative for $x$ values between -1 and 2, hence the solution is $x \in (-1, 2)$.

Solve x2−x−2<0x ^ { 2 } - x - 2 < 0x2−x−2<0

Solve $x ^ { 2 } - x - 2 < 0$