Determine the values of k for which the function f(x)=4x^2-3x+2kx+1 has two zeros. Check these values in the orginal equation.

Answer 1

If there are two distinct roots, the determinant is positive:

(-3+2k)^2 - 4(4)(1) > 0
9 - 12k + 4k^2 - 16 > 0
4k^2 - 12k -7 > 0
(2k+1)(2k-7) > 0
Either both factors are positive or both are negative
k < -1/2 or k > 7/2

Answer 2

where does 12k come from