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if (x+m) is the HCF of the functions x^2+ax+b & x^2+cx+d then show that their LCM is x^3+(a+c-m)x^2+(ac-m^2)x+m(a-m)(c-m)

if (x+m) is the HCF of the functions x^2+ax+b & x^2+cx+d then show that their LCM is x^3+(a+c-m)x^2+(ac-m^2)x+m(a-m)(c-m)

Grade:10

1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
8 years ago
HCF*LCM=(x^2+ax+b )* (x^2+cx+d)
(x+m)*LCM=x^4+(a+c)x^3+(b+d)x^2+bd
LCM=x^4+(a+c)x^3+(b+d)x^2+bd/((x+m))
dividing gives
LCM=x^3+(a+c-m)x^2+(ac-m^2)x+m(a-m)(c-m)

sher mohammad
b.tech, iit delhi

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