Question

fill in the blank so that the resulting statement is true.

an equation that can be written in the general form \\(ax^2 + bx + c = 0\\), \\(a \
eq 0\\) is called a equation.

options:
rational
linear
quadratic

Explanation:

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<reasoning>

Identify the given equation form

Using the Quadratic Equations knowledge point
\[
ax^2 + bx + c = 0, \quad a
eq 0
\]

Classify the polynomial degree

Using the Quadratic Equations knowledge point
The highest exponent of the variable \(x\) is 2, which defines a second-degree polynomial equation.

Determine the correct terminology

Using the Quadratic Equations knowledge point
A second-degree polynomial equation of this form is defined as a quadratic equation.
</reasoning>

<answer>
An equation that can be written in the general form \(ax^2 + bx + c = 0\), \(a
eq 0\) is called a <blank>quadratic</blank> equation.
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Equations"
]
}
</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

Identify the given equation form

Using the Quadratic Equations knowledge point
\[
ax^2 + bx + c = 0, \quad a
eq 0
\]

Classify the polynomial degree

Using the Quadratic Equations knowledge point
The highest exponent of the variable \(x\) is 2, which defines a second-degree polynomial equation.

Determine the correct terminology

Using the Quadratic Equations knowledge point
A second-degree polynomial equation of this form is defined as a quadratic equation.
</reasoning>

<answer>
An equation that can be written in the general form \(ax^2 + bx + c = 0\), \(a
eq 0\) is called a <blank>quadratic</blank> equation.
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Equations"
]
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