First slide

Theory of equations

Question

$Consider the equation x^{2} + 2 x - n = 0, where n \in N and n \in [5, 100] . Total number of different values of n so that$
$the given equation has integral roots is$

Moderate

A

8
B

3
C

6
D

4

Solution

$\begin{array}{l} x^{2} + 2 x - n = 0 \Rightarrow (x + 1)^{2} = n + 1 \\ \Rightarrow x = - 1 \pm \sqrt{n + 1} \end{array}$
$\begin{array}{l} Thus n + 1 should be a perfect square. \\ Since n \in [5, 100] \Rightarrow n + 1 \Rightarrow [6, 101] \end{array}$
$Perfect square values of n + 1 are 9, 16, 25, 36, 49, 64, 81, 100 .$
$Hence number of values are 8 .$

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