Which of the following represent the solution set of the given inequation?
−x2+2x+15>0; x∈R
Given: −x2+2x+15>0
Rule: If both the sides of an inequation are multiplied or divided by the same negative number, then the sign of the inequality will get reversed.
On multiplying the above inequation by -1, we get
⇒x2−2x−15<0
⇒x2−5x+3x−15<0
⇒(x+3)(x−5)<0
For this to happen, there will be two cases.
Case 1: x+3>0 and x−5<0
Which gives x>−3 and x<5
Case 2: x+3<0 and x−5>0
Which gives x<−3 and x>5. This is never possible.
So, the solution set is {x:x>−3 and x<5∀x∈R}