Question

Sa se determine m, astfel incat x^2-2mx+m(1+m)=0
a) sa aiba radacini egale
b) sa aiba radacini reale diferite
c) sa nu aiba radacini reale
x^2- x la puterea a2a

Answer 1

$\Delta=(-2m)^2-4m(1+m)=4m^2-4m-4m^2=-4m. \\ \\ a)~O~ecuatie~de~gradul~2~are~doua~radacini~reale~egale~daca ~\Delta=0. \\ \\ Deci~-4m=0 \Rightarrow \boxed{m=0}~. \\ \\ b)~O~ecuatie~de~gradul~2~are~doua~radacini~reale~diferite~daca ~ \Delta\ \textgreater \ 0. \\ \\ Deci~-4m\ \textgreater \ 0 \Rightarrow \boxed{m \in \big( - \infty~;~0 \big)}~. \\ \\ c)~O~ecuatie~de~gradul~2~nu~are~solutii~reale~daca~ \Delta\ \textless \ 0. \\ \\ Deci~-4m\ \textless \ 0 \Rightarrow \boxed{m \in \big(0; + \infty \big) }~.$