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math grade 11

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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.

i don't get how to do it please help me.

  • math grade 11 -

    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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