Question
find the roots of the equation.
6x^2 + 3x=0
6x^2 + 3x=0
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Answered by
GPT-4o mini
To find the roots of the equation \(6x^2 + 3x = 0\), we can factor the equation.
First, we can factor out the common term \(3x\):
\[
3x(2x + 1) = 0
\]
Now, we can set each factor equal to zero:
1. \(3x = 0\)
2. \(2x + 1 = 0\)
From \(3x = 0\), we find:
\[
x = 0
\]
From \(2x + 1 = 0\), we can solve for \(x\):
\[
2x = -1 \\
x = -\frac{1}{2}
\]
Therefore, the roots of the equation \(6x^2 + 3x = 0\) are:
\[
x = 0 \quad \text{and} \quad x = -\frac{1}{2}
\]
First, we can factor out the common term \(3x\):
\[
3x(2x + 1) = 0
\]
Now, we can set each factor equal to zero:
1. \(3x = 0\)
2. \(2x + 1 = 0\)
From \(3x = 0\), we find:
\[
x = 0
\]
From \(2x + 1 = 0\), we can solve for \(x\):
\[
2x = -1 \\
x = -\frac{1}{2}
\]
Therefore, the roots of the equation \(6x^2 + 3x = 0\) are:
\[
x = 0 \quad \text{and} \quad x = -\frac{1}{2}
\]
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