First slide

Theory of expressions

Question

If roots of the equation $x^{2} - 2 m x + m^{2} - 1 = 0$ lie in the interval (– 2, 4), then

Moderate

A

$- 1 < m < 3$
B

1 < m < 5
C

1 < m < 3
D

– 1 < m < 5

Solution

$x^{2} - 2 m x + m^{2} - 1 = 0 \Rightarrow (x - m)^{2} = 1$
$\Rightarrow x - m = \pm 1 \Rightarrow x = m \pm 1$
Therefore, $- 2 < m - 1 < m + 1 < 4$
$\Rightarrow - 1 < m < 3$

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