Question

- Find the values of 'm' for which x2 + 3xy + x + my - m has two linear factors in x and y, with integer coefficients.

Answer 1

we know
if ax^2+2hxy+by^2+2gx+2fy+c=0 represent straight lines equations
then
abc+2fgh-af^2-bg^2-ch^2=0
use above concept to solve this question
x^2+3xy+x+my-m=0
=> 1.0. (-m)+2(1/2).(m/2).3/2-1.(m/2)^2-0.(1/2)^2-(-m)(3/2)^2=0

=>0+3m/4-m^2/4-0+9m/4=0
=> m^2+12m=0
=> m (m+12)=0
=> m=0,-12

Answer 2

Refer The Attachment ⬆️

$\green{\sf{@MrMonarque}}$

Hope It Helps You ✌️