Anna L.

asked • 11/25/16

# What's the total number of possible integer solutions for this equation?

If k is a positive integer less than 17, what's the total number of possible integer solutions for the equation x2+8x+k=0?

## 1 Expert Answer

By:

David W. answered • 11/25/16

Tutor
4.7 (89)

Experienced Prof

Kenneth S.

However, if the problem really intended to use the word “solve” meaning “values of x that makes the equation true for an integer value of k of 1-16”.” Then the “solutions” are 1, 2, 3, 4, 5, 6, 7. That’s 7 (of course) and this interpretation seems super simple.
All solutions of the equation will be negatives, because (per Descartes' rule of signs) there can be no positive real zeros.
These solutions are {-1,-7) when k = 7
{-2,-6} when k = 12
{-3,-5} when k = 15
{-4 double root} when k = 16.
To summarize, there are four possible k values that generate integer solutions for the stated quadratic equation, and there are 7 solutions, in all, considering all of these k values.
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11/25/16

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