First slide

Theory of equations

Question

If $x^{2} + 2 x + 2 xy + my - 3$ has two rational factors, then the value of m will be

Moderate

A

$- 6, - 2$
B

$- 6, 2$
C

$6, - 2$
D

$6, 2$

Solution

Given expression $x^{2} + 2 x + 2 xy + my - 3$ can be written as $x^{2} + 2 x (1 + y) + (my - 3)$
But factors are rational, so $B^{2} - 4 AC$ is perfect square.
Now $4 {{(1 + y)}^{2} - (my - 3)} \geq 0$
$\Rightarrow 4 {y^{2} + 1 + 2 y - m + 3} \geq 0 \Rightarrow y^{2} + 2 y - my + 4 \geq 0$
Hence $2 y - m = \pm 4 y {as it is perfect square}$
$\Rightarrow 2 y - my = 4 y \Rightarrow m = - 2 .$
Now taking $(-)$ sign, we get $m = 6 .$

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