Question

Determinati absicsele punctelor de intersectie a graficului functiei F: R-> R, F(x)=3x la a doua +5x-2 cu axa Ox

Answer 1

[tex]f: \mathbb{R} \to \mathbb{R}~~,f(x) =3x^2+5x-2 \\ \\ Gf \cap OX = {A(X;0) \iff f(x) = 0 \\ \\ \text{Avem o ecuatie de gradul II } \\ \\ \\ 3x^2+5x-2 = 0 \\ \\ a=3 \\ b=5 \\ c=-2 \\ \\ \Delta = b^2-4ac \\ \Delta = 25-24 \\ \Delta = 1 \\ \\ x_1 = \dfrac{-b-\sqrt{\Delta}}{2a} \\ \\ x_1 = \dfrac{-5-1}{6}=\dfrac{-6}{6}=-1 \\ \\ \\ x_2 = \dfrac{-b+\sqrt{\Delta}}{2a} \\ \\ x_2 = \dfrac{-5+1}{6}=\dfrac{-4}{6}=\dfrac{-2}{3} \\ \\ \\ \\ \Rightarrow \boxed {A(-1;0) \text{ si } B(\dfrac{-2}{3};0)}[/tex]