Question

# Find the roots of  $$3x^2\,-\,11x\,+\,6\,=\,0$$

A
3,23
B
3,23
C
3,23
D
3,23

Solution

## The correct option is A $$\displaystyle\,3,\,\frac{2}{3}$$$$3x^2-11x+6=0$$$$\therefore 3x^2-9x-2x+6=0$$$$\therefore 3x(x-3)-2(x-3)=0$$$$\therefore (3x-2)(x-3)=0$$$$\therefore x=3$$ and $$x=\dfrac{2}{3}$$Mathematics

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The text contains a quadratic equation problem and its solution, with multiple choice options provided. The solution is given step-by-step, leading to the correct answer.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Question

# Find the roots of  $$3x^2\,-\,11x\,+\,6\,=\,0$$

A
3,23
B
3,23
C
3,23
D
3,23

Solution

## The correct option is A $$\displaystyle\,3,\,\frac{2}{3}$$$$3x^2-11x+6=0$$$$\therefore 3x^2-9x-2x+6=0$$$$\therefore 3x(x-3)-2(x-3)=0$$$$\therefore (3x-2)(x-3)=0$$$$\therefore x=3$$ and $$x=\dfrac{2}{3}$$Mathematics

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user
The text contains a quadratic equation problem and its solution, with multiple choice options provided. The solution is given step-by-step, leading to the correct answer.

TYPE: SINGLE_QUESTION_WITH_ANSWER