Question

Find the values of m' for which 2 + 3xy +x+ my-m has two linear factors in and y,
with integer coefficients.​

Answer 1

Answer:

Step-by-step explanation:

Let x  

2

+3xy+x+my−m=(ax+by+c)(ex+fy+g)

∴x  

2

+3xy+x+my−m=(ax+by+c)(ex+g)

or x  

2

+3xy+x+my−m=aex  

2

+bexy+cex+agx+bgy+cg

Equating the coefficients :

ae=1...(1)   be=3...(2)   ce+ag=1...(3)

bg=m...(4)   cg=−m...(5)

Then. from eq (1)(2) a=e=1,b=3

Putting in eq (3):e+g=1...(6)

Now,  

c

b

​  

=−1 or c=−b,c=−3

From eg (6), −3+9=1 or g=4

Putting in (5) : −m=−3×4⇒m=12  

solution

Answer 2

Step-by-step explanation:

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