Math Is Fun Forum

Avva

Member

Registered: 2009-02-25

Posts: 41

Algebra - roots of the equation

If the roots of the equation ax^2+bx+c=0 are α , β and                                                               if the roots of the equation a′x^2+b′x+c′=0 are (α +γ) , (β+γ) , prove that :
a′^2(b^2-4ac)=a^2+(b′^2-4a′c′)

coffeeking

Member

Registered: 2007-11-18

Posts: 44

Re: Algebra - roots of the equation

Well I suspect the last line should read:

I not sure if there are simpler method but this is what I have:

Since

are the roots of

and

are the roots of

we'll have:

By expanding and comparing coefficient of both equation we'll get:

Together, we'll get:

Since

, we'll only need to prove that

By expanding and substituting

We'll get

Which completes the proof.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Algebra - roots of the equation

That is not correct.

The equations should be

Last edited by JaneFairfax (2009-04-26 07:20:55)

coffeeking

Member

Registered: 2007-11-18

Posts: 44

Re: Algebra - roots of the equation

Oh my gosh! Think I am drunk lol
Hi Jane, thanks for correcting me. Please ignore my previous post. It's late in the night, I'll work this question again tomorrow.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Algebra - roots of the equation

If the roots of the equation ax^2+bx+c=0 are α , β and  if the roots of the equation a′x^2+b′x+c′=0 are (α +γ) , (β+γ) , prove that :
a′^2(b^2-4ac)=a^2+(b′^2-4a′c′)dunno

roots

roots

since the roots of the second equation can be written as a function of the first roots, you can represent the second equation as a transformation of the first (or as i do it, the other way round)

Last edited by luca-deltodesco (2009-04-26 10:31:07)

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Avva

Member

Registered: 2009-02-25

Posts: 41

Re: Algebra - roots of the equation

TX 4 everyone appreciated