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For some real numbers a and b, the equation 8x^3 + 4ax^2 + 2bx + a = 0 has three distinct positive roots. If the sum of the base-2 logarithms of the roots is 5, what is the value of a?

 Aug 12, 2019
 #1
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Let the roots  be   x, y , z

 

So

 

 [ log  2 x  +  log 2  y  + log 2  z ]  = 5

 log 2  (xyz)  = 5

2^5  = xyz

xyz  = 32

 

And the  product of the  roots =  -a/ 8

 

xyz  = -a / 8

32 = -a / 8

256 = - a

a  = -256

 

 

cool cool cool

 Aug 12, 2019

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