Determine os valores de m para que a função f(x) = -x² -4x – (-m +1) assuma valores negativos para todo x real.
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delta <0 para que a função assuma valores negativos, assim
a=-1 b=-4 c=-(-m+1)
![delta =(-4)^2-4.(-1).[-(-m+1)] \\ \\ delta = 16+4[m-1] \\ \\ delta = 16+4m-4 \\ \\ delta = 4m+12 \\ \\ 4m+12\ \textless \ 0 \\ \\ 4m\ \textless \ -12 \\ \\ m\ \textless \ \frac{-12}{4} \\ \\ m\ \textless \ -3](https://tex.z-dn.net/?f=delta+%3D%28-4%29%5E2-4.%28-1%29.%5B-%28-m%2B1%29%5D+%5C%5C++%5C%5C+delta+%3D+16%2B4%5Bm-1%5D+%5C%5C++%5C%5C+delta+%3D+16%2B4m-4+%5C%5C++%5C%5C+delta+%3D+4m%2B12+%5C%5C++%5C%5C+4m%2B12%5C+%5Ctextless+%5C+0+%5C%5C++%5C%5C+4m%5C+%5Ctextless+%5C+-12+%5C%5C++%5C%5C+m%5C+%5Ctextless+%5C++%5Cfrac%7B-12%7D%7B4%7D++%5C%5C++%5C%5C+m%5C+%5Ctextless+%5C+-3 "delta =(-4)^2-4.(-1).[-(-m+1)] \\ \\ delta = 16+4[m-1] \\ \\ delta = 16+4m-4 \\ \\ delta = 4m+12 \\ \\ 4m+12\ \textless \ 0 \\ \\ 4m\ \textless \ -12 \\ \\ m\ \textless \ \frac{-12}{4} \\ \\ m\ \textless \ -3")
a=-1 b=-4 c=-(-m+1)
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