If $x^{3} - m x^{2} - 3 x + 2 = 0$ has two roots equal in magnitude but opposite in sign, then $m$ is:

\frac{3}{2}

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\frac{2}{3}

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- \frac{2}{3}

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none of these

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Solution

The correct option is B $\frac{2}{3}$
Let $α, - α, β$ be the roots of $x^{3} - m x^{2} - 3 x + 2 = 0$
Then
$s_{1} = α - α + β = m \Rightarrow β = m$
Substituting $x = m$ in equation, we get
$m^{3} - m . m^{2} - 3. m + 2 = 0 \Rightarrow m = \frac{2}{3}$
Hence, option 'B' is correct.

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