Given,

Polynomial 3x² + 4x + 2k

Zero of the polynomial = – 2

As we have zero,

f(x) = 3x² + 4x + 2k = 0

By putting x = – 2

f( – 2) = 3( – 2)² + 4 ( – 2) + 2k = 0

f( – 2) = 12 – 8 + 2k = 0

= 4 + 2k = 0

= 2k = – 4

k = – 4/2 = – 2

So we have the value of k = – 2