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Mathematics
Helena
26 April, 18:27
13. Solve: 3x² + 11x + 5<9
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Sophia Reese
26 April, 18:40
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-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
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