Question

Which of the following represent the solution set of the given inequation?

$-x^2+2x+15>0;x\in \text{R}$

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Given: $-x^2+2x+15>0$

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

$\Rightarrow x^2-2x-15<0$


$\Rightarrow x^2-5x+3x-15<0$

$\Rightarrow (x+3)(x-5)<0$

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 $\{x:x>-3andx<5\forall x\in R\}$