Question

Find the solution set of <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $x^2-5x-6>0$

• A. $x<-1$ or $x>6$
• B. $x<1$ or $x>6$
• C. $x<6$ or $x>-1$
• D. $x>-1$ or $x<6$

Answer 1

The correct option is A $x<-1$ or $x>6$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $x^2-5x-6>0$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $x^2-6x+x-6>0$

$x(x-6)+1(x-6)>0$

$(x-6)(x+1)>0)$

Case -1

$(x-6)>0$ and $(x+1)>0$

$x>6$ and $x>-1$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\Rightarrow$ $x>6$

Case -2

$(x-6)<0$ and $(x+1)<0$

$x<6$ and $x<-1$

$\Rightarrow$ $x<-1$

Hence the final solution is $x<-1$ or $x>6$