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
B
2
C
2
D
3

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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