Question

question

for the following quadratic equation, find the discriminant.

\\8x^2 - 20x - 89 = 4x^2 + 6\\

Explanation:

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<reasoning>

Rearrange the equation into standard form

\[

$$\begin{aligned} 8x^2 - 20x - 89 &= 4x^2 + 6 \\ 4x^2 - 20x - 95 &= 0 \end{aligned}$$

\]

Identify the coefficients

\[

$$\begin{aligned} a &= 4 \\ b &= -20 \\ c &= -95 \end{aligned}$$

\]

Calculate the discriminant

\[

$$\begin{aligned} D &= b^2 - 4ac \\ D &= (-20)^2 - 4(4)(-95) \\ D &= 400 + 1520 \\ D &= 1920 \end{aligned}$$

\]
</reasoning>

<answer>
1920
</answer>

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Answer:

<pre_analysis>
{
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],
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</pre_analysis>

<reasoning>

Rearrange the equation into standard form

\[

$$\begin{aligned} 8x^2 - 20x - 89 &= 4x^2 + 6 \\ 4x^2 - 20x - 95 &= 0 \end{aligned}$$

\]

Identify the coefficients

\[

$$\begin{aligned} a &= 4 \\ b &= -20 \\ c &= -95 \end{aligned}$$

\]

Calculate the discriminant

\[

$$\begin{aligned} D &= b^2 - 4ac \\ D &= (-20)^2 - 4(4)(-95) \\ D &= 400 + 1520 \\ D &= 1920 \end{aligned}$$

\]
</reasoning>

<answer>
1920
</answer>

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"Mathematics",
"Algebra",
"Quadratic Discriminant"
]
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