Determine the values of k for which the function f(x)=4x^2-3x+2kx+1 has 2 zeros

Answer 1

recall that the formula for discriminant:
D = b^2 - 4ac
if
D < 0 : two imaginary roots
D = 0 : one root
D > 0 : two real roots
thus, given the equation, we can substitute the values of a, b and c in the discriminant, which must be > 0:
(2k - 3)^2 - 4(4)(1) > 0
4k^2 - 12k + 9 - 16 > 0
4k^2 - 12k - 7 > 0
(2k - 7)(2k + 1) > 0
these are the ranges of values:
k > 7/2
k < -1/2

hope this helps~ :)