Question

If x a set of all real numbers R the find the solution set for $(x-3)(x+5)<0$

• A. $[3,\infty )$
• B. $(-5,3)$
• C. $[-5,\infty )$
• D. $[-5,3]$

Answer 1

The correct option is B $(-5,3)$

Case 1 :
When (x-3) > 0 and (x+5) <0
i.e. x > 3 and x < -5
This is not possible as as a number greater than 3 cannot be less than -5

Case 2:
When (x-3) < 0 and (x+5) > 0
i.e. x < 3 and x > -5
-5 < x < 3, which is possible.
Therefore Solution set = $(-5,3)$