Proof involving polynomial inequality

[Guest]

Hi guys,

I am having difficulties solving the following problem set:

"Let

[tex]f(\alpha )=x^n+\beta_{n-1}+...+\beta_1x+\beta_0[/tex]

be a polynomial with real coefficients and only real roots. Proove that

[tex]f(\alpha)p''(\alpha)\le p'(x)^2[/tex]

for all [tex]x\in R[/tex]."

I have unsuccessfully tried to express the polynomial in different ways and then using proof by induction on its degree, of which I am sure should work.

Any help is higly appreciated.

Thanks,

/A

[Math Tutor]

You should define p(x)

[Guest]

You should define p(x)

Ooops! The p's should be replaced by f's...

However, I have managed to solve the problem. Therefore, help is no longer needed.

[Guest]

Could you write the proof, please?

[Guest]

Proof involving polynomial inequality

Postby Guest » Thu Nov 10, 2011 9:04 pm
Hi guys,

I am having difficulties solving the following problem set: