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

Answer:

MATHS

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Asked on December 26, 2019 by

Naveen Anki

Find the values of 'm' for which x

2

+3xy+x+my−m has two linear factors in x and y, with integer coefficients.

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ANSWER

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