Math, asked by SakshamBrilliantKid, 1 year ago

If f(x)=
$(x - 2)( {x }^{2} - x - a)$
and g(x)=
$(x + 2)( {x}^{2} + x - b)$
and their HCF is
${x}^{2} - 4$
then find the value of (a-b) where a and b are constants.

SakshamBrilliantKid: Please help me with this question.

Answers

Answered by δΙΔΔΗλΣΓΗΛ

★ POLYNOMIALS AND RATIONAL EXPRESSIONS ★

$f(x) = (x - 2)(x {}^{2} - x - a) \\ g(x) = (x + 2)(x {}^{2} + x - b) \\$
H.C.F. = x² - 4 = ( x +2 ) ( x -2 )

Hence ( x + 2 ) is a factor of ( x² - x - a )

Which yields ; a = 6

Similarly for ( x - 2 )

Which gives b = 6

Hence , a - b = 6 - 6 = 0

SakshamBrilliantKid: why x+2 is a factor of (x^2-x-a) ??

δΙΔΔΗλΣΓΗΛ: Full of HCF is Highest Common Factor , and it's clearly mentioned that factor of f(x) and g(x) is x² - 4 , so , it's a factor ,

δΙΔΔΗλΣΓΗΛ: full form*

SakshamBrilliantKid: so it should also be a factor of (x-2) as in f(x)

SakshamBrilliantKid: why it's only for the second term ?

δΙΔΔΗλΣΓΗΛ: Then the HCF and polynomialic system will collapse to zero , to avoid that we pick 2nd factor

SakshamBrilliantKid: ohk

SakshamBrilliantKid: thank u

SakshamBrilliantKid: you in india

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If f(x)=and g(x)= and their HCF is then find the value of (a-b) where a and b are constants.

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If f(x)=
$(x - 2)( {x }^{2} - x - a)$
and g(x)=
$(x + 2)( {x}^{2} + x - b)$
and their HCF is
${x}^{2} - 4$
then find the value of (a-b) where a and b are constants.