Question

13. Solve: 3x² +11x +5<9

Answer 1

Answer:

-4<x<1/3

Step-by-step explanation:

3x²+11x+5<9

3x²+11x-4<0.

First we determine the solutions of

3x²+11x-4=0

Delta=11²-4×3×(-4)=121+48=169=13²

The roots are

x1=(-11-13)/6=-24/6=-4

x2=(-11+13)/6=2/6=1/3

So, we have:

3x²+11x-4=3(x-⅓)(x+4)=(3x-1)(x+4)

So, coming back to our inequality:

(3x-1)(x+4)<0, we note (as we already know) that this condition is satisfied for all those x located between the roots: -4<x<1/3