Determine the value of k *please help!! I have a math unit test on april 7th!*

Question

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

Answer 1

4x² + (2k-3)x + 1 = 0

 

The quadratic has two zeros if the discriminant, B² - 4AC,  is nonzero.

 

A = 4, B = 2k-3, C = 1

 

(2k-3)²  - 4(4)(1) ≠ 0

 

4k² - 12k + 9 - 16 ≠ 0

 

4k² - 12k - 7 ≠ 0

 

(2k + 1)(2k - 7) ≠ 0

 

k ≠ -1/2, 7/2