question:

Find all values of K such that the equation 4x (to the power of 2) + 6x +k = 0 has imaginary roots.

Use the discriminant, b^{2}-4ak

If it is < 0, then there are no real roots.

In other words, solve 6^{2}-4(4)c<0\Rightarrow 36-16k<0 for k.