SOLUTION: Please help me solve this problem: Find the value of k. {{{6x^2+kx-6=0}}} ; one root is the negative reciprocal of the other. Can I also ask for the solution? Thank you very mu

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me solve this problem: Find the value of k. {{{6x^2+kx-6=0}}} ; one root is the negative reciprocal of the other. Can I also ask for the solution? Thank you very mu      Log On


   

Question 222372: Please help me solve this problem:
Find the value of k.
6x%5E2%2Bkx-6=0 ; one root is the negative reciprocal of the other.
Can I also ask for the solution?
Thank you very much.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

This has a "surprise" answer:

6x%5E2%2Bkx-6=0

The solutions by the quadratic equation are:

x+=+%28-k+%2B-+sqrt%28+k%5E2-4%2A%286%29%2A-6%29+%29%2F%282%2A6%29+ 

x+=+%28-k+%2B-+sqrt%28+k%5E2-4%2A%286%29%2A-6%29+%29%2F%282%2A6%29+ 

x+=+%28-k+%2B-+sqrt%28+k%5E2%2B144%29+%29%2F12+ 

So there are two solutions:

(-k + sqrt( k^2+144) )/12 and (-k - sqrt( k^2+144) )/12

Any number times its negative reciprocal must equal -1.

So we multiply these two roots and set the product 
equal to -1:



Multiply using "FOIL"

%28+%28k%5E2+-+%28+k%5E2%2B144%29+%29%2F144%29=-1

%28+%28k%5E2+-++k%5E2-144+%29%2F144%29=-1

+-144%2F144=-1

-1=-1

Since this comes out an identity, that means that
k can be any number whatsoever, and in every
case one root will be the negative reciprocal of
the other!

Edwin