First slide

Theory of equations

Question

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

Moderate

A

-2
B

1
C

2
D

none of these

Solution

$Let α be the root of x^{2} - x + m = 0 and 2 α$ be the root of $x^{2} - 3 x + 2 m = 0$ . Then,
$α^{2} - α + m = 0 and 4 α^{2} - 6 α + 2 m = 0$
Eliminating $α, m^{2} = - 2 m \Rightarrow m = 0, m = - 2$

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