Question

Primul subpunct, vreau o idee va rog

Answer 1

Răspuns:

Ca f(x) sa aibe valori pozitive => a>0 si delta<=0

$f(x)=ax^2+6(a+1)x+9a+31$

$a=a;b=6(a+1);c=9a+31$

Prima conditie: a>0

A doua:

$Delta\leq 0$

$(6a+6)^2-4a(9a+31)\leq 0$

$36a^2+72a+36-36a^2-124a\leq 0$

$-52a+36\leq 0$

$-52a\leq -36$

$52a\geq 36=>a\geq \frac{9}{13}$

$=> a$∈$[\frac{9}{13};+inf)$