QQuestionMathematics
QuestionMathematics
What is the solution to $3 x^{2}+ 5 x>- 2$ ?
A. $x<- 1$ or $x>-\frac{2}{3}$
B. $x \geq-\frac{2}{3}$ or $x<1$
C. $-\frac{2}{3} \leq x \leq 1$
D. $-\frac{2}{3}>x>- 1$
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Answer
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Step 1:I'll solve this step by step using precise LaTeX formatting:
Step 2:: Rearrange the inequality
• Start with $$3x^{2} + 5x > -2
• Rearrange to standard quadratic form: 3x^{2} + 5x + 2 > 0
Step 3:: Solve the quadratic
• $$= 25 - 24 = 1
• Use the discriminant method
Step 4:: Find roots
• Root 2: $$\frac{-5 - 1}{6} = -1
• = \frac{- 5 \pm \sqrt{1}}{2(3)}
Step 5:: Determine solution
• Therefore, $$x < -1$$ or $$x > -\frac{2}{3}
• Solution is outside the roots
Final Answer
A. x < - 1 or x > -\frac{2}{3}
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