Engineering Board Exam Reviewer · Inequalities and Absolute Value · hard

Find all values of k for which x2+kx+9>0 for every real x.

1. -6<k<6
2. k<-6 or k>6
3. -3<k<3
4. k>0

Answer

A. -6<k<6

Solution

The parabola opens upward, so it stays above the axis exactly when the discriminant is negative: k2-36<0 -6<k<6.

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