Polynomial transformation (1 Viewer)

[monstylez]

For polynomial transformation, how would i go around doing x = a+(1/a) ?

Thanks in advance.

 

[tommykins]

Tried it, couldn't do it myself.

 

[shaon0]

For polynomial transformation, how would i go around doing x = a+(1/a) ?

Thanks in advance.

I'll have a crack... even though i don't know polynomial transformation.
x=(a^2+1)/a
ax=a^2+1
a^2-ax+1=0

 

[tommykins]

I'll have a crack... even though i don't know polynomial transformation.
x=(a^2+1)/a
ax=a^2+1
a^2-ax+1=0

hrm so a = x +- sqrt (x²-4)/2

Seems farfetched, but will try.

 

[conics2008]

wtf poly transofrmation ???

 

[shaon0]

hrm so a = x +- sqrt (x²-4)/2

Seems farfetched, but will try.

oh using quadratic formula.

 

[tommykins]

wtf poly transofrmation ???

Given a polynomial as ax^3 + bx^2+ cx + d has roots x,y,z (cbf alpha etc.)

Find the polynomial with roots x/2, y/2, z/2.

That's polynomial transformation.

 

[hon1hon2hon3]

I will put in an attempt . . . simple one like x = x^2 . We know we have to sub x = root (x) .

So for this one . lets say . . . x = x + (1/x) (a or x , to me is the same thing)

and now let the root we need to be y

x = y ( this is what we are finding )

x = x + (1/x)

sooo we sub the secound one into the top one , soo its like

y = x + 1/x

y - 1/x = x

and y = x

so x = x - 1/x (this is the root we need)

got answer to check @@? this is what it think thought . . . does it make sense to any one ? or i am wrong ? Peace

 

[tommykins]

回复: Re: Polynomial transformation

Makes no sense to me.

Can someone clarify please? 3unitz/affinity?

 

[conics2008]

Re: 回复: Re: Polynomial transformation

hey with those i think it only works with quadratic questions.

i remember doing something like that.. thats like finding the NEW poly with the given roots....

yeah those only work with quadratic how you have to manaully put them in eg

x^2 + (a+b)x+ab where ab are the roots...

 

[tommykins]

回复: Re: 回复: Re: Polynomial transformation

hey with those i think it only works with quadratic questions.

i remember doing something like that.. thats like finding the NEW poly with the given roots....

yeah those only work with quadratic how you have to manaully put them in eg

x^2 + (a+b)x+ab where ab are the roots...

No, it works for all polynomials.

They don't give you the roots, only give you them as alpha, beta, gamma etc.

 

[conics2008]

Re: 回复: Re: 回复: Re: Polynomial transformation

No, it works for all polynomials.

They don't give you the roots, only give you them as alpha, beta, gamma etc.

I know what you mean..

eg find the new poly with roots a^2-1

you just equate x=a^2-1 and make a the subject.. but in that case.. its hard to do..

doing it with quadratic is a pain.. i dont think you would be expected to do with a cubic or quad poly...

eg ax^2+bx+c=0 find the new poly with roots a+1/a, b +1/b

you can use the sum of roots and product of roots... but doing it with a cubic is a pain..

are you understanding what im sayin??

 

[tommykins]

回复: Re: 回复: Re: 回复: Re: Polynomial transformation

I know what you mean..

eg find the new poly with roots a^2-1

you just equate x=a^2-1 and make a the subject.. but in that case.. its hard to do..

doing it with quadratic is a pain.. i dont think you would be expected to do with a cubic or quad poly...

eg ax^2+bx+c=0 find the new poly with roots a+1/a, b +1/b

you can use the sum of roots and product of roots... but doing it with a cubic is a pain..

are you understanding what im sayin??

Yes but cubics aren't too hard, they normally use cubics so that you get an x.sqrtx anyways.

but yeah using a quad to find a isannoying.

thanks anyways