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Question

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

x2+2x+15>0; xR


A

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B

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C

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D

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Solution

The correct option is C


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

x22x15<0


x25x+3x15<0

(x+3)(x5)<0

For this to happen, there will be two cases.

Case 1: x+3>0 and x5<0

Which gives x>3 and x<5

Case 2: x+3<0 and x5>0

Which gives x<3 and x>5. This is never possible.

So, the solution set is {x:x>3 and x<5xR}


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