If the two roots of the quadratic 4x^2+7x+k$ are $\frac{-7\pm i\sqrt{15}}{8}$, what is $k$?
\(\frac{-7\pm i\sqrt{15}}{8} \)
4x^2 + 7x + k
The product of the roots = k/4
So
-7 + i √15 - 7 - i √15
________ * ___________ =
8 8
49 - i^2 (15) 49 + 15 64
__________ = ________ = _____ = 1
64 64 64
1 = k/4
k = 4
