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If the sum of the reciprocals of the roots of the quadratic \(3x^2+7x+k=0\) is \(7/3\), what is \(k\)?

 Apr 29, 2022
 #1
avatar+122385 
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3x^2  + 7x + k  = 0

 

Let  the roots  be  a  and b

 

So

 

1/a + 1/b =  7/3

 

(a + b) / ab  = 7/3

 

The product of the roots  =   k/3

 

So

 

ab =  k/3

 

So

 

(a + b)  / (k/3)   =  7/3

 

3 (a + b)  =  (7/3)k

 

a + b  =  (7/9)k

 

And the sum of the roots =   -7/3

 

So

 

(-7/3) = (7/9)k

 

k =  (-7/3) / (7/9)  =  -3

 

cool cool cool

 Apr 29, 2022
 #2
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+1

Thank You!

 Apr 29, 2022

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