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C4-Partial fractions. Comparing Coeff

x^4-3x^3+5x^2-3x+6=x(x-2)^2(x+1)+A(x-2)(x+1)+B(x+1)+C(x-2)^2

I got

B=4

C=2

when comparing coeff of

x^2

to find A

I get

5=-2+A+C

Meaning

A=5

however the book has it down as

A=3

Am i wrong?

(edited 6 years ago)

Reply 1

RDKGames

Study Forum Helper

Original post by joyoustele

x^4-3x^3+5x^2-3x+6=x(x-2)^2(x+1)+A(x-2)(x+1)+B(x+1)+C(x-2)^2

I got

B=4

C=2

when comparing coeff of

x^2

to find A

I get

5=-2+A+C

Meaning

A=5

however the book has it down as

A=3

Am i wrong?

Yeah.

Did the first one in my head but the coeff of x^2 should be 0, not -2, if I’m not mistaken. Check it

Reply 2

the bear

Original post by joyoustele

x^4-3x^3+5x^2-3x+6=x(x-2)^2(x+1)+A(x-2)(x+1)+B(x+1)+C(x-2)^2

I got

B=4

C=2

when comparing coeff of

x^2

to find A

I get

5=-2+A+C

Meaning

A=5

however the book has it down as

A=3

Am i wrong?

yes you are wrong. if you let x = 0 , B = 4 & C = 2 then you get A = 3

Reply 3

joyoustele

Original post by the bear

yes you are wrong. if you let x = 0 , B = 4 & C = 2 then you get A = 3

Yh, i should have tried this too.

Reply 4

the bear

Original post by joyoustele

Yh, i should have tried this too.

as a lazy person i would use x = 0 as it is less work :teehee:

Reply 5

joyoustele

Original post by RDKGames

Yeah.

Did the first one in my head but the coeff of x^2 should be 0, not -2, if I’m not mistaken. Check it

x(x-2)^2(x+1)

x^2-4x+2(x+1)x

x(x^3-3x^2-2x+2)

x^4-3x^3-2x^2+2x

Coeff of

x^2 =-2

+ coeff of C

x^2

I know its A=3 now, but i cant see where i went wrong here

Reply 6

joyoustele

Original post by the bear

as a lazy person i would use x = 0 as it is less work :teehee:

Yh, I shall start doing that. :smile:

Reply 7

RDKGames

Study Forum Helper

Original post by joyoustele

x(x-2)^2(x+1)

x^2-4x+2(x+1)x

x(x^3-3x^2-2x+2)

x^4-3x^3-2x^2+2x

Coeff of

x^2 =-2

+ coeff of C

x^2

I know its A=3 now, but i cant see where i went wrong here

Second line. Constant of the expanded quadraric is 4, not 2.

Reply 8

joyoustele

Original post by RDKGames

Second line. Constant of the expanded quadraric is 4, not 2.

oh.

-TY

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