13. Solve: 3x² + 11x + 5<9

Question

Mathematics

Helena

26 April, 18:27

13. Solve: 3x² + 11x + 5<9

+5

Answers (1)

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Sophia Reese · Answer 1

-4
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