For what values of k will the function f(x)=3x^2+4x+k=0 have no zeros, one zero, 2 zeros

Answer 1

you will have to look at the discriminant b^2 - 4ac

b^2-4ac = 16 - 4(3)(k) = 16 - 12k

If 16-12k = 0 you have one zero
if 16 - 12k > 0 you have 2 zeros
if 16-12k < 0 you have no zeros

solve each case to find the corresponding value of k