First slide

Theory of expressions

Question

All the values of m for which both the roots of the equation x² - 2mx + m² - 1 - 0 are greater than -2 but less than 4,then m is in the interval

Moderate

A

$- 2 < m < 0$
B

m > 3
C

$- 1 < m < 3$
D

$1 < m < 4$

Solution

The given equation is
$x^{2} - 2 mx + m^{2} - 1 = 0 \Rightarrow (x - m)^{2} - 1 = 0 \Rightarrow (x - m + 1) (x - m - 1) = 0 \Rightarrow x = m - 1, m + 1$
From given condition,
$\begin{aligned} m - 1 > - 2 and m + 1 < 4 \\ \Rightarrow m > - 1 and m > 3 \\ Hence, - 1 < m < 3 \end{aligned}$

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