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Question

The value of $$m$$ for which one of the roots of $$x^{2} - 3x + 2m = 0$$ is double of one of the roots of $$x^{2} - x + m = 0$$, is


A
4
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B
2
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C
2
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D
3
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Solution

The correct option is B $$-2$$
Let $$\alpha$$ be the roots of $$x^{2} - x + m = 0$$ and $$2\alpha$$ be the root of $$x^{2} - 3x + 2m = 0$$.

Then, $$\alpha^{2} - \alpha + m = 0$$

and $$4\alpha^{2} - 6\alpha + 2m = 0$$

On solving these equations, we get

$$\dfrac {\alpha^{2}}{-2m + 6m} = \dfrac {\alpha}{4m - 2m} = \dfrac {1}{-6 + 4}$$

$$\Rightarrow \dfrac {\alpha^{2}}{4m} = \dfrac {\alpha}{2m} = \dfrac {1}{-2}$$

$$\Rightarrow \alpha^{2} = -2m$$ and $$\alpha = -m$$

$$\therefore (-m)^{2} = -2m$$

$$\Rightarrow m^{2} + 2m = 0$$

$$\Rightarrow m(m + 2) = 0$$

$$\Rightarrow m = 0, m = -2$$.

Mathematics

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