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 tie in the interval

Moderate

A

$- 2 < m < 0$
B

m > 3
C

$- 1 < m < 3$
D

1 < m < 4

Solution

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

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App