Question

$|3x^{2} +5x-2| \leq 2$

Answer 1

-2≤3x²+5x-2≤2

3x²+5x≥0
x(3x+5)≥0
x1=-5/3
x2=0
x∈(-∞;-5/3]∪[0;∞)  (1)


3x²+5x-4≤0
x1,2=(-5+-√(25+48))/6

x1,2=(-5+-√73)/6

x∈[(-5-√73)/6;(-5+√73)/6}  (2)


comnditiile (1) si (2) trebuiesc intersectate

rezulta x∈[(-5-√73)/6;-5/3]∪[0;(-5+√73)/6]