Logarithms of the Zeros of a QuadraticDate: 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 |
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