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### Logarithms of the Zeros of a Quadratic

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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.

```

```
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?

- 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

thank you!

Mary
```
Associated Topics:
High School Logs
High School Polynomials

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