Question

Fie f:R -> R, f(x) = x^2 + mx + 3, m ∈ R. Determinati valorile parametrului real m astfel incat Gf ∩ Ox ≠ ∅ .

Answer 1

[tex]G_f \cap Ox \neq \O\Rightarrow $ Ecuatia $ f(x) = 0 $, are solutii. \\ \\ $f(x) = 0 \Rightarrow x^2+mx+3 = 0, $ $ $ are solutii reale, conditia este \Delta \geq 0. \\ \\ \Delta \geq 0 \Rightarrow m^2-4\cdot 3 \geq 0 \Rightarrow m^2-12 \geq0 \Rightarrow m^2\geq 12\Big|\sqrt {}\Rightarrow \\ \\ \Rightarrow \sqrt{m^2} \geq 2\sqrt3 \Rightarrow |m|\geq 2\sqrt 3 \Rightarrow \left\| \begin{array}{c} m \leq -2\sqrt 3 \\ $sau$\\m\geq 2\sqrt 3 \end{array} \right \Rightarrow [/tex]

$\Rightarrow \boxed{m\in (-\infty, -2\sqrt 3] \cup [2\sqrt 3,+\infty)}$