Question

determine the value of k for which the fuction f(x)=4x^2-3x+2kx+1 has 2 zeros.

Answer 1

To have 2 zeros, or two real solutions, the discriminant must be positive
for 4x^2 - 3x + 2kx + 1
a = 4
b = 2k-3
c = 1

b^2 - 4ac > 0
(2k-3)^2 - 4(4)(1) > 0
4k^2 - 12k -7 > 0
(2k + 1)(2k - 7) > 0
<b>k < -1/2 OR k > 7/2</b>

You might want to put that into the interval notation you have been taught.