math
posted by Annie on .
Determine the values of k for which the function f(x)= 4x^23x+2kx+1 has two zeros , check these values in the original equation

to have two zeros, either real or complex,
b^2  4ac ≠ 0
4x^2 + x(2k  3) + 1
discrim. = (2k3)^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.