[tex]f = x^4-3x^2+m \\ \\ x^2 = t,\quad t\geq 0 \\ \\ f = t^2-3t+m,\quad t \geq 0 \\ \\ \Delta \geq 0\quad \text{si}\quad f(0) \geq 0, \,\,\text{fiindca daca f(0)}< 0, \text{ ecuatia cu t va avea}\\ \text{doar o solutie.} \\ \\ 9 - 4m \geq 0\quad \text{si}\quad m \geq 0 \Leftrightarrow -4m \geq -9}\quad \text{si}\quad m \leq 0\Leftrightarrow \\ \\ \Letfrightarrow m \leq \dfrac{9}{4}\quad \text{si}\quad m\geq 0 \Rightarrow \boxed{m\in \Big[0,\dfrac{9}{4}\Big]}[/tex]
