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Polynomial Roots Question (Further Maths)
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Could anyone point me in the right direction of how to start this?
Solve 32z3 - 14z + 3 = 0 given that one root is twice one of the others.
Solve 32z3 - 14z + 3 = 0 given that one root is twice one of the others.
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#2
(Original post by beachpanda)
Could anyone point me in the right direction of how to start this?
Solve 32z3 - 14z + 3 = 0 given that one root is twice one of the others.
Could anyone point me in the right direction of how to start this?
Solve 32z3 - 14z + 3 = 0 given that one root is twice one of the others.
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(Original post by Haywood1743)
use your alpha beta gama equations but have gamma equal to 2 alpha
use your alpha beta gama equations but have gamma equal to 2 alpha
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#4
(Original post by beachpanda)
Got it - unsure where I've gone wrong here though?
Got it - unsure where I've gone wrong here though?
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(Original post by DFranklin)
Don't forget you need to divide by the coefficient of z^3. (i.e. your calculations would be valid if that coefficient was 1, but it isn't).
Don't forget you need to divide by the coefficient of z^3. (i.e. your calculations would be valid if that coefficient was 1, but it isn't).
(Original post by Haywood1743)
use your alpha beta gama equations but have gamma equal to 2 alpha
use your alpha beta gama equations but have gamma equal to 2 alpha
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My textbook also says for this separate question that the sum of alpha, beta, gamma, delta for this equation is positive 2, not negative 2.
Does that look correct? I thought it was negative 2
Does that look correct? I thought it was negative 2
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#7
(Original post by beachpanda)
My textbook also says for this separate question that the sum of alpha, beta, gamma, delta for this equation is positive 2, not negative 2.
Does that look correct? I thought it was negative 2
My textbook also says for this separate question that the sum of alpha, beta, gamma, delta for this equation is positive 2, not negative 2.
Does that look correct? I thought it was negative 2
It is +2.
If you expand
your final term is 
In general:
Sum of roots works out -ve
Sum of product of 2 roots works out +ve
Sum of product of 3 roots works out -ve
Sum.....4 roots is +ve
and it carries on alternating.
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(Original post by ghostwalker)
I presume you mean the final term; the product of all four roots.
It is +2.
If you expand your final term is
In general:
Sum of roots works out -ve
Sum of product of 2 roots works out +ve
Sum of product of 3 roots works out -ve
Sum.....4 roots is +ve
and it carries on alternating.
I presume you mean the final term; the product of all four roots.
It is +2.
If you expand
your final term is In general:
Sum of roots works out -ve
Sum of product of 2 roots works out +ve
Sum of product of 3 roots works out -ve
Sum.....4 roots is +ve
and it carries on alternating.
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#9
(Original post by beachpanda)
Cool got it, thanks!
Cool got it, thanks!
and less easily confused with 
. If, as here, you're dealing with quartics, where a general quartic is often written "x^4 + ax^3 + bx^2 + cx + d" I feel there's quite a real risk of confusion.As someone who struggled a lot with handwriting at A-level I know it's annoying to get these comments, but I did find myself that it was worth making the effort.
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(Original post by DFranklin)
On a side note, I'm going to be annoying and *suggest* you think about trying to write your alphas so they look more like and less easily confused with . If, as here, you're dealing with quartics, where a general quartic is often written "x^4 + ax^3 + bx^2 + cx + d" I feel there's quite a real risk of confusion.
As someone who struggled a lot with handwriting at A-level I know it's annoying to get these comments, but I did find myself that it was worth making the effort.
On a side note, I'm going to be annoying and *suggest* you think about trying to write your alphas so they look more like
and less easily confused with . If, as here, you're dealing with quartics, where a general quartic is often written "x^4 + ax^3 + bx^2 + cx + d" I feel there's quite a real risk of confusion.As someone who struggled a lot with handwriting at A-level I know it's annoying to get these comments, but I did find myself that it was worth making the effort.
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