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Logarithms of the Zeros of a Quadratic


Date: 03/24/2002 at 21:29:55
From: Mary
Subject: Logarithms of the zeros of a quadratic

The question I am trying to solve is:

If p and q are the zeros of 2x^2-mx+1 = 0, what is the value of 
log(base 2)p + log(base 2)q?

I don't know where to start. I was thinking of solving the quadratic 
equation for x and then putting those values into the p and q, but I 
cannot isolate x. I would appreciate any help even if it is just to 
get me pointed in the right direction.  

Thanks in advance.


Date: 03/25/2002 at 08:35:07
From: Doctor Paul
Subject: Re: Logarithms of the zeros of a quadratic

It is a somewhat well known theorem that says: if the roots of a 
quadratic polynomial ax^2 + bx + c = 0 are P and Q, then PQ = c/a and 
P + Q = -b/a.

I use log[2](P) to represent log(base 2)P.

Then log[2](P) + log[2](Q) = log[2](PQ) = log[2](c/a) = 

log[2](c) - log[2](a)

Does this help?

Please write back if you'd like to talk about this some more.

- Doctor Paul, The Math Forum
  http://mathforum.org/dr.math/   


Date: 04/03/2002 at 20:38:41
From: Mary
Subject: Logarithms of the zeros of a quadratic

Thanks for your help.  Your answer was right on the money!  Thank you 
thank you!  

Mary
    
Associated Topics:
High School Logs
High School Polynomials

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