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If the two roots of the quadratic $3x^2+5x+k$ are $\frac{-5\pm i\sqrt{11}}{6}$, what is $k$?

 May 4, 2018
 #1
avatar+94545 
+1

\(\frac{-5\pm i\sqrt{11}}{6}\)

 

3x^2 + 5x + k

 

The product  of the two  roots  is

 

(-5 + i√11) / 6  *    (-5 - i√11) / 6    =    (25  - i^2* 11)/ 36 =   (25 - (-1)(11) ) / 36  =

 

[25 + 11] / 36    =   36 / 36   =    1

 

And this product will  equal  k/3

 

So

 

k/3  =  1         multiply both sides by 3

 

k  = 3

 

 

 

cool cool cool

 May 4, 2018

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