A poly question ! is there a shorter method ?! (1 Viewer)

[iampeterr]

8x^3 - 36x^2 + 22x + 11
where alpha, beta and gamma are in arithmetic series, find alpha,beta and gamma,

is there any shorter way to do this ? maybe more based on series ? instead of poly itself ?

thanks

 

[bleakarcher]

8x^3-36x^2+22x+11=0
Let the roots be A-B, A, A+B since they are in arithmetic series.
By the sum and products of roots:
=>3A=36/8=9/2
:.A=3/2
A(A-B)(A+B)=-11/8
But A=3/2,
=>3[(3/2)-B][(3/2)+B]=-11/4
(3/2)^2-B^2=-11/12
B^2=(9/4)+(11/12)=19/6
B=sqrt(19/6)
Hence the roots are: (3/2)-sqrt(19/6), 3/2, (3/2)+sqrt(19/6)

 

[SpiralFlex]

8x^3-36x^2+22x+11=0
Let the roots be A-B, A, A+B since they are in arithmetic series.
By the sum and products of roots:
=>3A=36/8=9/2
:.A=3/2
A(A-B)(A+B)=-11/8
But A=3/2,
=>3[(3/2)-B][(3/2)+B]=-11/4
(3/2)^2-B^2=-11/12
B^2=(9/4)+(11/12)=19/6
B=sqrt(19/6)
Hence the roots are: (3/2)-sqrt(19/6), 3/2, (3/2)+sqrt(19/6)

I think the OP was trying to avoid this method.

 

[bleakarcher]

well when i read his post, he said the equation has roots A, B and C, i thought he didnt know of the fact the roots so be simplified so that there are only two pronumerals.

 

[iampeterr]

yeah haha i was looking for a method if it exists to do something more series based then poly :S

 

[bleakarcher]

sorry dude, i wouldnt know of any.

 

[Drongoski]

8x^3 - 36x^2 + 22x + 11
where alpha, beta and gamma are in arithmetic series, find alpha,beta and gamma,

is there any shorter way to do this ? maybe more based on series ? instead of poly itself ?

thanks

should read: arithmetic sequence and not series.

 

[bleakarcher]

^ mind explaining?

 

[iampeterr]

i think his correcting my grammatical error !

 

[bleakarcher]

lol i know that, i want to know the difference between a series and a sequence.

 

[Shadowdude]

A sequence is something like {1, 2, 3, ...} or {a, a+d, a+2d,...} like in the question.

A series is when you add the terms of a sequence, that is 1+2+3+... or a+(a+d)+(a+2d)+...

 

[bleakarcher]

ah yeh thanks man

 

[Drongoski]

A sequence is something like {1, 2, 3, ...} or {a, a+d, a+2d,...} like in the question.

A series is when you add the terms of a sequence, that is 1+2+3+... or a+(a+d)+(a+2d)+...

Thanks. Saved me having to explain the difference.

 

[Drongoski]

i think his correcting my grammatical error !

No - it is not a grammatical error! But "his" is.

 

[dest]

No worries boys, the answer is:
8======D