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Determine the values of k for which the function f(x)= 4x^2-3x+2kx+1 has two zeros , check these values in the original equation

  • math -

    to have two zeros, either real or complex,
    b^2 - 4ac ≠ 0

    4x^2 + x(2k - 3) + 1

    discrim. = (2k-3)^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.

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