UPSC CDS Math Quadratic Equations and Inequations Questions

In order to find the critical points, we have to convert the given inequality into an equation.∴x2−6x−27=0
⇒(x−9)(x+3)=0
Critical points are 9 and –3
Now test the given inequality by taking points left and right of these points.
When x>9
(x−9)(x+3)>0
when x<0 but >−3
(x–9)(x+3)<0
When x<−3
Thus, the given inequality is true for x<−3 or x>9
(x–9)(x+3)>0