Quote (feanur @ Feb 11 2018 12:53pm)
The discriminant of your discriminant is 1-4*1*7 = -27 < 0
You have proven that your discriminant p²-p+7 never equals zero (for any real value of p).
It means that it is :
- either always positive,
- or always negative.
Try with p = 0 :
Δ = p²-p+7 = 7 in this case, hence : Δ > 0.
Conclusion 1 : Δ > 0, always.
Conclusion 2 : x²+2px+p=7 always has 2 real solutions (for any value of the real parameter p).
Thanks for the conclusions!
Makes sense.
