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

Answer 1

to have two zeros, either real or complex,
b^2 - 4ac ≠ 0

4x^2 + x(2k - 3) + 1

discrim. = (2k-3)^2 - 4(4)(1)
= 4k^2 - 12k + 9 - 16
= 4k^2 - 12k - 7

to have only 1 root
4k^2 - 12k - 7 = 0
(2k - 7)(2k + 1) = 0
k = 7/2 or k = -1

So to have two roots, k ≠ 7/2 or k ≠ -1

So put any value of k other than those two and you will get 2 differentroots.