Question

Stabileste semnul functiei f:R→R , f(x)=-3x²+2x+8

Answer 1

Răspuns: f(x)>0 pentru x€(-4/3;2)

f(x)<0 pentru x€(-inf;-4/3)U(2;+inf)

Explicație pas cu pas: f(x)>0 <=> -3x^2+2x+8>0 <=> $3x^{2} -2x-8<0 <=> delta=4+96=100 \left \{ {{x1=\frac{2-10}{6}=\frac{-8}{6}=- \frac{4}{3} } \atop {x=\frac{2+10}{6}=\frac{12}{6}=2 }} \right.$ x€(-4/3;2)

f(x)<0<=> -3x^2+2x+8<0 <=> $3x^{2} -2x-8>0 <=> delta=4+96=100 \left \{ {{x1=\frac{2-10}{6}=\frac{-8}{6}=- \frac{4}{3} } \atop {x=\frac{2+10}{6}=\frac{12}{6}=2 }} \right.$ x€(-inf;-4/3)U(2;+inf)