Question

Solution of inequality $(x-1{)}^2(x+1{)}^3(x-4)<0$ is

• A. $-1<x<3$
• B. $-2<x<4$
• C. $-1<x<4$
• D. $-1<x<2$

Answer 1

The correct option is C $-1<x<4$

Given, ${\left(x1\right)}^2{(x+1)}^3\left(x4\right)<0$
Since square of a number cannot be $<0$
This means, one of ${(x+1)}^3$ or $\left(x4\right)$ is $<0$
Now, ${(x+1)}^3<0$ and $x-4>0$ => $x<-1$ and $x>4$ --- (1)
OR ${(x+1)}^3>0$ and $x-4<0$ => $x>-1$ and $x<4$ --- (2)
From solutions of both possibilities, $-1<x<4$