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I have the following equation


Delta is negative but the equation should always be positive, how can I notice the latter observation? I mean: I've been solving this for half an hour (checking if I had made a mistake) without success and then noticed that the equation is always positive, how can I determine if an equation is always positive when the delta is <0? Is there any rule?

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up vote 1 down vote accepted

If the discriminant ($\Delta$) of the quadratic is negative then it always keeps the same sign. As for $p = 0$ it is positive then...

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