SOLUTION: If the two roots of the quadratic 7x^2+3x+k$ are (-3±isqrt(299))/14, what is k?

 is the product of the roots (Vieta's theorem):

 =  =  = .


Hence, k =  = 11.


Thanks to @MathTherapy for pointing my typo in my previous version.

Product of the roots = 

Roots:  =====>  and  

We then get: 

Reducing, we get: 

 ------ Cross-multiplying