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If the roots of the given equation $2 x^2+3(\lambda-2) x+\lambda+4=0$ be equal in magnitude but opposite in sign, then $\lambda=$
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The correct answer is:
$2$
Let roots are $\alpha$ and $-\alpha$, then sum of the roots
$\alpha+(-\alpha)=\frac{3(\lambda-2)}{2} \Rightarrow 0=\frac{3}{2}(\lambda-2)$
$\Rightarrow \lambda=2$
$\alpha+(-\alpha)=\frac{3(\lambda-2)}{2} \Rightarrow 0=\frac{3}{2}(\lambda-2)$
$\Rightarrow \lambda=2$
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