Question

The greatest negative integer satisfying $x^2-4x-77<0$ and $x^2>4$ is...

Answer 1

$-3.(x+7)(x-ll)<0,(x+2)(x-2)>0$ $\therefore$

$-7<x<11andx<-2orx>2$

Mark these regions on real line and take their intersection.

The intersection of two regions is given by

$-7<x<-2or2<x<11$

We are to find the greatest - ive integer.

Hence we choose $-7<x<-2$.

Therefore all negative integers -6 to - 3 will satisfy the above and the greatest amongst these is - 3.