# Find the range of values of K satisfying the inequality?

The inequality is K^2 + 9K + 14 > 0

What are the range of values of K satisfying the inequality??

### 2 Answers

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• mizoo
Lv 7
7 years ago
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k^2 + 9k + 14 > 0

(k + 2)(k + 7) > 0

k > -2 or k < -7

in the interval notation : (-∞, -7) U (-2, ∞)

• Hosam
Lv 6
7 years ago

First factor the quadtratic given as (K+7)(K+2) , so now you have

(K+7)(K+2) > 0

Since the coefficient of K^2 is positive, the quadratic is positive if K is OUTSIDE the interval between the two roots (-7) and (-2) . This interval can be written as [-7,-2]

So the range of K = R / [-7,-2] = (-inf, -7) U (-2, inf )

where inf means infinity.

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