Question

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

• A. $-6$
• B. $-7$
• C. $-8$
• D. $-17$

Answer 1

Answer: (A)

$-6$

Since $x^2-4x-77<0$

$\Rightarrow x^2-11x+7x-77<0$

$\Rightarrow (x-11)(x+7)<0$

$\therefore -7<x<11$ ...(1)

Also, $x^2>4$

$\Rightarrow x^2-4>0$

$\therefore x<-2$ or $x>2$ ...(2)

Using (1) and (2), we have

$\therefore$ The gratest negative interger satisfying the above inequality is $-6$.