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I need help with this question

determine the values in k for which the function f(x)= 4x^2-3x+2kx+1 has two zeros. Check these values in the original equation.

F(x) = Y = 4x^2 - 3x + 2kx + 1.

This problem was solved by using EXCEL spread sheets and trial & error.

First, I temporarily ignored the 3rd term (2kx); and I changed b (the coefficient of x) until I found the required zeroes. Then I calculated the corresponding value of k:

b = -3 + 2k = 5,
-3 + 2k = 5,
2k = 5 + 3,
2k = 8,
k = 8 / 2 = 4.

5 was chosen for b because it gave 2
zeroes.

So when k = 4: (-1 , 0) , (-1/4 , 0).

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