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Find the values of 'm' for which *-+3ay +x +m- m has two linear factors in a and ywith integer coefficients. |
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Answer» Let, x²+3xy+x+my-m=(ax+by+c)(ex+fy+g)Since the given expression does not contain y² then one of the linear factors must not contain the term containing y. Therefore,x²+3xy+x+my-m=(ax+by+c)(ex+g)or, x²+3xy+x+my-m=aex²+bexy+cex+agx+bgy+cgEquating the coefficients from both sides,ae=1 ----------------------(1)be=3 ----------------------(2)ce+ag=1 -----------------(3)bg=m ---------------------(4)cg=-m --------------------(5)Since all the coefficients are integers then from (1),a=e=1∴, from (2), b=3Putting in(3),c+g=1 ----------------(6)Now dividing (4) by (5),b/c=-1or, c=-bor, c=-3∴, from (6),-3+g=1or, g=4Putting in (5),-m=-3×4or, m=12 Ans. |
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